@article{53341,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The Cauchy problem in <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathbb {R}^n$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:msup>
                    <mml:mrow>
                      <mml:mi>R</mml:mi>
                    </mml:mrow>
                    <mml:mi>n</mml:mi>
                  </mml:msup>
                </mml:math></jats:alternatives></jats:inline-formula> is considered for the Keller–Segel system <jats:disp-formula><jats:alternatives><jats:tex-math>$$\begin{aligned} \left\{ \begin{array}{l}u_t = \Delta u - \nabla \cdot (u\nabla v), \\ 0 = \Delta v + u, \end{array} \right. \qquad \qquad (\star ) \end{aligned}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mtable>
                      <mml:mtr>
                        <mml:mtd>
                          <mml:mrow>
                            <mml:mfenced>
                              <mml:mrow>
                                <mml:mtable>
                                  <mml:mtr>
                                    <mml:mtd>
                                      <mml:mrow>
                                        <mml:msub>
                                          <mml:mi>u</mml:mi>
                                          <mml:mi>t</mml:mi>
                                        </mml:msub>
                                        <mml:mo>=</mml:mo>
                                        <mml:mi>Δ</mml:mi>
                                        <mml:mi>u</mml:mi>
                                        <mml:mo>-</mml:mo>
                                        <mml:mi>∇</mml:mi>
                                        <mml:mo>·</mml:mo>
                                        <mml:mrow>
                                          <mml:mo>(</mml:mo>
                                          <mml:mi>u</mml:mi>
                                          <mml:mi>∇</mml:mi>
                                          <mml:mi>v</mml:mi>
                                          <mml:mo>)</mml:mo>
                                        </mml:mrow>
                                        <mml:mo>,</mml:mo>
                                      </mml:mrow>
                                    </mml:mtd>
                                  </mml:mtr>
                                  <mml:mtr>
                                    <mml:mtd>
                                      <mml:mrow>
                                        <mml:mrow />
                                        <mml:mn>0</mml:mn>
                                        <mml:mo>=</mml:mo>
                                        <mml:mi>Δ</mml:mi>
                                        <mml:mi>v</mml:mi>
                                        <mml:mo>+</mml:mo>
                                        <mml:mi>u</mml:mi>
                                        <mml:mo>,</mml:mo>
                                      </mml:mrow>
                                    </mml:mtd>
                                  </mml:mtr>
                                </mml:mtable>
                              </mml:mrow>
                            </mml:mfenced>
                            <mml:mspace />
                            <mml:mspace />
                            <mml:mrow>
                              <mml:mo>(</mml:mo>
                              <mml:mo>⋆</mml:mo>
                              <mml:mo>)</mml:mo>
                            </mml:mrow>
                          </mml:mrow>
                        </mml:mtd>
                      </mml:mtr>
                    </mml:mtable>
                  </mml:mrow>
                </mml:math></jats:alternatives></jats:disp-formula>with a focus on a detailed description of behavior in the presence of nonnegative radially symmetric initial data <jats:inline-formula><jats:alternatives><jats:tex-math>$$u_0$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:msub>
                    <mml:mi>u</mml:mi>
                    <mml:mn>0</mml:mn>
                  </mml:msub>
                </mml:math></jats:alternatives></jats:inline-formula> with non-integrable behavior at spatial infinity. It is shown that if <jats:inline-formula><jats:alternatives><jats:tex-math>$$u_0$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:msub>
                    <mml:mi>u</mml:mi>
                    <mml:mn>0</mml:mn>
                  </mml:msub>
                </mml:math></jats:alternatives></jats:inline-formula> is continuous and bounded, then (<jats:inline-formula><jats:alternatives><jats:tex-math>$$\star $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mo>⋆</mml:mo>
                </mml:math></jats:alternatives></jats:inline-formula>) admits a local-in-time classical solution, whereas if <jats:inline-formula><jats:alternatives><jats:tex-math>$$u_0(x)\rightarrow +\infty $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:msub>
                      <mml:mi>u</mml:mi>
                      <mml:mn>0</mml:mn>
                    </mml:msub>
                    <mml:mrow>
                      <mml:mo>(</mml:mo>
                      <mml:mi>x</mml:mi>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                    <mml:mo>→</mml:mo>
                    <mml:mo>+</mml:mo>
                    <mml:mi>∞</mml:mi>
                  </mml:mrow>
                </mml:math></jats:alternatives></jats:inline-formula> as <jats:inline-formula><jats:alternatives><jats:tex-math>$$|x|\rightarrow \infty $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mo>|</mml:mo>
                    <mml:mi>x</mml:mi>
                    <mml:mo>|</mml:mo>
                    <mml:mo>→</mml:mo>
                    <mml:mi>∞</mml:mi>
                  </mml:mrow>
                </mml:math></jats:alternatives></jats:inline-formula>, then no such solution can be found. Furthermore, a collection of three sufficient criteria for either global existence or global nonexistence indicates that with respect to the occurrence of finite-time blow-up, spatial decay properties of an explicit singular steady state plays a critical role. In particular, this underlines that explosions in (<jats:inline-formula><jats:alternatives><jats:tex-math>$$\star $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mo>⋆</mml:mo>
                </mml:math></jats:alternatives></jats:inline-formula>) need not be enforced by initially high concentrations near finite points, but can be exclusively due to large tails.</jats:p>}},
  author       = {{Winkler, Michael}},
  issn         = {{2296-9020}},
  journal      = {{Journal of Elliptic and Parabolic Equations}},
  keywords     = {{Applied Mathematics, Numerical Analysis, Analysis}},
  number       = {{2}},
  pages        = {{919--959}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity}}},
  doi          = {{10.1007/s41808-023-00230-y}},
  volume       = {{9}},
  year         = {{2023}},
}

@article{53539,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The infinite Brownian loop on a Riemannian manifold is the limit in distribution of the Brownian bridge of length <jats:italic>T</jats:italic> around a fixed origin when <jats:inline-formula><jats:alternatives><jats:tex-math>$$T \rightarrow +\infty $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                <mml:mrow>
                  <mml:mi>T</mml:mi>
                  <mml:mo>→</mml:mo>
                  <mml:mo>+</mml:mo>
                  <mml:mi>∞</mml:mi>
                </mml:mrow>
              </mml:math></jats:alternatives></jats:inline-formula>. The aim of this note is to study its long-time asymptotics on Riemannian symmetric spaces <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic> of noncompact type and of general rank. This amounts to the behavior of solutions to the heat equation subject to the Doob transform induced by the ground spherical function. Unlike the standard Brownian motion, we observe in this case phenomena which are similar to the Euclidean setting, namely <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                <mml:msup>
                  <mml:mi>L</mml:mi>
                  <mml:mn>1</mml:mn>
                </mml:msup>
              </mml:math></jats:alternatives></jats:inline-formula> asymptotic convergence without requiring bi-<jats:italic>K</jats:italic>-invariance for initial data, and strong <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^{\infty }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                <mml:msup>
                  <mml:mi>L</mml:mi>
                  <mml:mi>∞</mml:mi>
                </mml:msup>
              </mml:math></jats:alternatives></jats:inline-formula> convergence.</jats:p>}},
  author       = {{Papageorgiou, Efthymia}},
  issn         = {{2296-9020}},
  journal      = {{Journal of Elliptic and Parabolic Equations}},
  keywords     = {{Applied Mathematics, Numerical Analysis, Analysis}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Asymptotics for the infinite Brownian loop on noncompact symmetric spaces}}},
  doi          = {{10.1007/s41808-023-00250-8}},
  year         = {{2023}},
}

@article{45956,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>The full Maxwell equations in the unbounded three-dimensional space coupled to the Landau–Lifshitz–Gilbert equation serve as a well-tested model for ferromagnetic materials.
We propose a weak formulation of the coupled system based on the boundary integral formulation of the exterior Maxwell equations.
We show existence and partial uniqueness of a weak solution and propose a new numerical algorithm based on finite elements and boundary elements as spatial discretization with backward Euler and convolution quadrature for the time domain.
This is the first numerical algorithm which is able to deal with the coupled system of Landau–Lifshitz–Gilbert equation and full Maxwell’s equations without any simplifications like quasi-static approximations (e.g. eddy current model) and without restrictions on the shape of the domain (e.g. convexity).
We show well-posedness and convergence of the numerical algorithm under minimal assumptions on the regularity of the solution.
This is particularly important as there are few regularity results available and one generally expects the solution to be non-smooth.
Numerical experiments illustrate and expand on the theoretical results.</jats:p>}},
  author       = {{Bohn, Jan and Feischl, Michael and Kovács, Balázs}},
  issn         = {{1609-4840}},
  journal      = {{Computational Methods in Applied Mathematics}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Numerical Analysis}},
  number       = {{1}},
  pages        = {{19--48}},
  publisher    = {{Walter de Gruyter GmbH}},
  title        = {{{FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation}}},
  doi          = {{10.1515/cmam-2022-0145}},
  volume       = {{23}},
  year         = {{2022}},
}

@article{50024,
  author       = {{Feng, Yuanhua and Gries, Thomas and Letmathe, Sebastian and Schulz, Dominik}},
  issn         = {{2073-4859}},
  journal      = {{The R Journal}},
  keywords     = {{Statistics, Probability and Uncertainty, Numerical Analysis, Statistics and Probability}},
  number       = {{1}},
  pages        = {{182--195}},
  publisher    = {{The R Foundation}},
  title        = {{{The smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series}}},
  doi          = {{10.32614/rj-2022-017}},
  volume       = {{14}},
  year         = {{2022}},
}

@article{34075,
  author       = {{Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{2325-3444}},
  journal      = {{Mathematics and Mechanics of Complex Systems}},
  keywords     = {{Computational Mathematics, Numerical Analysis, Civil and Structural Engineering}},
  number       = {{1}},
  pages        = {{21--50}},
  publisher    = {{Mathematical Sciences Publishers}},
  title        = {{{A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics}}},
  doi          = {{10.2140/memocs.2022.10.21}},
  volume       = {{10}},
  year         = {{2022}},
}

@article{50025,
  author       = {{Feng, Yuanhua and Gries, Thomas and Letmathe, Sebastian and Schulz, Dominik}},
  issn         = {{2073-4859}},
  journal      = {{The R Journal}},
  keywords     = {{Statistics, Probability and Uncertainty, Numerical Analysis, Statistics and Probability}},
  number       = {{1}},
  pages        = {{182--195}},
  publisher    = {{The R Foundation}},
  title        = {{{The smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series}}},
  doi          = {{10.32614/rj-2022-017}},
  volume       = {{14}},
  year         = {{2022}},
}

@article{33649,
  author       = {{Kessler, Jan and Calcavecchia, Francesco and Kühne, Thomas}},
  issn         = {{2513-0390}},
  journal      = {{Advanced Theory and Simulations}},
  keywords     = {{Multidisciplinary, Modeling and Simulation, Numerical Analysis, Statistics and Probability}},
  number       = {{4}},
  publisher    = {{Wiley}},
  title        = {{{Artificial Neural Networks as Trial Wave Functions for Quantum Monte Carlo}}},
  doi          = {{10.1002/adts.202000269}},
  volume       = {{4}},
  year         = {{2021}},
}

@article{45951,
  author       = {{Kovács, Balázs}},
  issn         = {{0749-159X}},
  journal      = {{Numerical Methods for Partial Differential Equations}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Numerical Analysis, Analysis}},
  number       = {{3}},
  pages        = {{1093--1112}},
  publisher    = {{Wiley}},
  title        = {{{Computing arbitrary Lagrangian Eulerian maps for evolving surfaces}}},
  doi          = {{10.1002/num.22340}},
  volume       = {{35}},
  year         = {{2018}},
}

@article{45946,
  author       = {{Kovács, Balázs and Power Guerra, Christian Andreas}},
  issn         = {{0749-159X}},
  journal      = {{Numerical Methods for Partial Differential Equations}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Numerical Analysis, Analysis}},
  number       = {{2}},
  pages        = {{518--554}},
  publisher    = {{Wiley}},
  title        = {{{Maximum norm stability and error estimates for the evolving surface finite element method}}},
  doi          = {{10.1002/num.22212}},
  volume       = {{34}},
  year         = {{2017}},
}

@article{45945,
  author       = {{Kovács, Balázs and Power Guerra, Christian Andreas}},
  issn         = {{0749-159X}},
  journal      = {{Numerical Methods for Partial Differential Equations}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Numerical Analysis, Analysis}},
  number       = {{2}},
  pages        = {{518--554}},
  publisher    = {{Wiley}},
  title        = {{{Maximum norm stability and error estimates for the evolving surface finite element method}}},
  doi          = {{10.1002/num.22212}},
  volume       = {{34}},
  year         = {{2017}},
}

@article{45936,
  author       = {{Kovács, Balázs and Power Guerra, Christian Andreas}},
  issn         = {{0749-159X}},
  journal      = {{Numerical Methods for Partial Differential Equations}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Numerical Analysis, Analysis}},
  number       = {{4}},
  pages        = {{1200--1231}},
  publisher    = {{Wiley}},
  title        = {{{Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces}}},
  doi          = {{10.1002/num.22047}},
  volume       = {{32}},
  year         = {{2016}},
}

@article{45939,
  author       = {{Kovács, Balázs and Li, Buyang and Lubich, Christian}},
  issn         = {{0036-1429}},
  journal      = {{SIAM Journal on Numerical Analysis}},
  keywords     = {{Numerical Analysis, Applied Mathematics, Computational Mathematics}},
  number       = {{6}},
  pages        = {{3600--3624}},
  publisher    = {{Society for Industrial & Applied Mathematics (SIAM)}},
  title        = {{{A-Stable Time Discretizations Preserve Maximal Parabolic Regularity}}},
  doi          = {{10.1137/15m1040918}},
  volume       = {{54}},
  year         = {{2016}},
}

@article{45935,
  author       = {{Axelsson, Owe and Karátson, János and Kovács, Balázs}},
  issn         = {{0036-1429}},
  journal      = {{SIAM Journal on Numerical Analysis}},
  keywords     = {{Numerical Analysis, Applied Mathematics, Computational Mathematics}},
  number       = {{6}},
  pages        = {{2957--2976}},
  publisher    = {{Society for Industrial & Applied Mathematics (SIAM)}},
  title        = {{{Robust Preconditioning Estimates for Convection-Dominated Elliptic Problems via a Streamline Poincaré--Friedrichs Inequality}}},
  doi          = {{10.1137/130940268}},
  volume       = {{52}},
  year         = {{2014}},
}

@article{37667,
  author       = {{Rösler, Margit and Remling, Heiko}},
  issn         = {{0021-9045}},
  journal      = {{Journal of Approximation Theory}},
  keywords     = {{Applied Mathematics, General Mathematics, Numerical Analysis, Analysis}},
  pages        = {{30--48}},
  publisher    = {{Elsevier BV}},
  title        = {{{Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians}}},
  doi          = {{10.1016/j.jat.2014.07.005}},
  volume       = {{197}},
  year         = {{2014}},
}

@article{45416,
  author       = {{Mahnken, Rolf}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  keywords     = {{Applied Mathematics, General Engineering, Numerical Analysis}},
  number       = {{7}},
  pages        = {{1015--1036}},
  publisher    = {{Wiley}},
  title        = {{{An inverse finite-element algorithm for parameter identification of thermoelastic damage models}}},
  doi          = {{10.1002/(sici)1097-0207(20000710)48:7<1015::aid-nme912>3.0.co;2-4}},
  volume       = {{48}},
  year         = {{2005}},
}

@article{45433,
  author       = {{Mahnken, Rolf and Stein, E. and Bischoff, D.}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  keywords     = {{Applied Mathematics, General Engineering, Numerical Analysis}},
  number       = {{5}},
  pages        = {{1015--1029}},
  publisher    = {{Wiley}},
  title        = {{{A stabilization procedure by line-search computation for first order approximation strategies in structural optimization}}},
  doi          = {{10.1002/nme.1620350505}},
  volume       = {{35}},
  year         = {{2005}},
}

@article{45435,
  author       = {{Mahnken, Rolf and Stein, Erwin}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  keywords     = {{Applied Mathematics, General Engineering, Numerical Analysis}},
  number       = {{7}},
  pages        = {{1619--1633}},
  publisher    = {{Wiley}},
  title        = {{{Adaptive time-step control in creep analysis}}},
  doi          = {{10.1002/nme.1620280711}},
  volume       = {{28}},
  year         = {{2005}},
}

@article{39959,
  author       = {{Rösler, Margit and de Jeu, Marcel}},
  issn         = {{0021-9045}},
  journal      = {{Journal of Approximation Theory}},
  keywords     = {{Applied Mathematics, General Mathematics, Numerical Analysis, Analysis}},
  number       = {{1}},
  pages        = {{110--126}},
  publisher    = {{Elsevier BV}},
  title        = {{{Asymptotic Analysis for the Dunkl Kernel}}},
  doi          = {{10.1006/jath.2002.3722}},
  volume       = {{119}},
  year         = {{2002}},
}

@article{45425,
  author       = {{Johansson, Magnus and Mahnken, Rolf and Runesson, Kenneth}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  keywords     = {{Applied Mathematics, General Engineering, Numerical Analysis}},
  number       = {{11}},
  pages        = {{1727--1747}},
  publisher    = {{Wiley}},
  title        = {{{Efficient integration technique for generalized viscoplasticity coupled to damage}}},
  doi          = {{10.1002/(sici)1097-0207(19990420)44:11<1727::aid-nme568>3.0.co;2-p}},
  volume       = {{44}},
  year         = {{2002}},
}