@article{53345, abstract = {{AbstractA no-flux initial-boundary value problem for

ut=Δ(uϕ(v)),vt=Δv−uv,(⋆)is considered in smoothly bounded subdomains of

with

n⩾1

and suitably regular initial data, whereφis assumed to reflect algebraic type cross-degeneracies by sharing essential features with

0⩽ξ↦ξα

for some

α⩾1

. Based on the discovery of a gradient structure acting at regularity levels mild enough to be consistent with degeneracy-driven limitations of smoothness information, in this general setting it is shown that with some measurable limit profile

u∞

and some null set

N⋆⊂(0,∞)

, a corresponding global generalized solution, known to exist according to recent literature, satisfies

ρ(u(⋅,t))⇀⋆ρ(u∞)in L∞(Ω) and v(⋅,t)→0in Lp(Ω)for all p⩾1as

(0,∞)∖N⋆∋t→∞

, where

ρ(ξ):=ξ2(ξ+1)2

ξ⩾0

. In the particular case when either

n⩽2

and

α⩾1

is arbitrary, or

n⩾1

and

α∈[1,2]

, additional quantitative information on the deviation of trajectories from the initial data is derived. This is found to imply a lower estimate for the spatial oscillation of the respective first components throughout evolution, and moreover this is seen to entail that each of the uncountably many steady states

(u⋆,0)

of (

⋆

) is stable with respect to a suitably chosen norm topology.}}, author = {{Winkler, Michael}}, issn = {{0951-7715}}, journal = {{Nonlinearity}}, keywords = {{Applied Mathematics, General Physics and Astronomy, Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{8}}, pages = {{4438--4469}}, publisher = {{IOP Publishing}}, title = {{{Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction}}}, doi = {{10.1088/1361-6544/ace22e}}, volume = {{36}}, year = {{2023}}, } @article{53341, abstract = {{AbstractThe Cauchy problem in

$$\mathbb {R}^n$$

R n is considered for the Keller–Segel system

$$\begin{aligned} \left\{ \begin{array}{l}u_t = \Delta u - \nabla \cdot (u\nabla v), \\ 0 = \Delta v + u, \end{array} \right. \qquad \qquad (\star ) \end{aligned}$$

u t = Δ u - ∇ · ( u ∇ v ) , 0 = Δ v + u , ( ⋆ ) with a focus on a detailed description of behavior in the presence of nonnegative radially symmetric initial data

$$u_0$$

u 0 with non-integrable behavior at spatial infinity. It is shown that if

$$u_0$$

u 0 is continuous and bounded, then (

$$\star $$

⋆ ) admits a local-in-time classical solution, whereas if

$$u_0(x)\rightarrow +\infty $$

u 0 ( x ) → + ∞ as

$$|x|\rightarrow \infty $$

| x | → ∞ , 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 (

$$\star $$

⋆ ) need not be enforced by initially high concentrations near finite points, but can be exclusively due to large tails.}}, 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{53340, author = {{Painter, Kevin J. and Winkler, Michael}}, issn = {{0036-1399}}, journal = {{SIAM Journal on Applied Mathematics}}, keywords = {{Applied Mathematics}}, number = {{5}}, pages = {{2096--2117}}, publisher = {{Society for Industrial & Applied Mathematics (SIAM)}}, title = {{{Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities}}}, doi = {{10.1137/22m1539393}}, volume = {{83}}, year = {{2023}}, } @article{53342, author = {{Winkler, Michael and Yokota, Tomomi}}, issn = {{0022-0396}}, journal = {{Journal of Differential Equations}}, keywords = {{Analysis, Applied Mathematics}}, pages = {{1--28}}, publisher = {{Elsevier BV}}, title = {{{Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems}}}, doi = {{10.1016/j.jde.2023.07.029}}, volume = {{374}}, year = {{2023}}, } @article{53346, author = {{Winkler, Michael}}, issn = {{1079-9389}}, journal = {{Advances in Differential Equations}}, keywords = {{Applied Mathematics, Analysis}}, number = {{11/12}}, publisher = {{Khayyam Publishing, Inc}}, title = {{{Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing}}}, doi = {{10.57262/ade028-1112-921}}, volume = {{28}}, year = {{2023}}, } @article{53229, author = {{Santos-Arteaga, Francisco J. and Di Caprio, Debora and Tavana, Madjid and Tena, Emilio Cerda}}, issn = {{1063-6706}}, journal = {{IEEE Transactions on Fuzzy Systems}}, keywords = {{Applied Mathematics, Artificial Intelligence, Computational Theory and Mathematics, Control and Systems Engineering}}, number = {{2}}, pages = {{460--474}}, publisher = {{Institute of Electrical and Electronics Engineers (IEEE)}}, title = {{{A Credibility and Strategic Behavior Approach in Hesitant Multiple Criteria Decision-Making With Application to Sustainable Transportation}}}, doi = {{10.1109/tfuzz.2022.3188875}}, volume = {{31}}, year = {{2023}}, } @article{53539, abstract = {{AbstractThe infinite Brownian loop on a Riemannian manifold is the limit in distribution of the Brownian bridge of length T around a fixed origin when

$$T \rightarrow +\infty $$

T → + ∞ . The aim of this note is to study its long-time asymptotics on Riemannian symmetric spaces G/K 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

$$L^1$$

L 1 asymptotic convergence without requiring bi-K-invariance for initial data, and strong

$$L^{\infty }$$

L ∞ convergence.}}, 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{43105, author = {{Black, Tobias and Fuest, Mario and Lankeit, Johannes and Mizukami, Masaaki}}, issn = {{1468-1218}}, journal = {{Nonlinear Analysis: Real World Applications}}, keywords = {{Applied Mathematics, Computational Mathematics, General Economics, Econometrics and Finance, General Engineering, General Medicine, Analysis}}, publisher = {{Elsevier BV}}, title = {{{Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source}}}, doi = {{10.1016/j.nonrwa.2023.103868}}, volume = {{73}}, year = {{2023}}, } @article{44077, author = {{Maack, Marten}}, issn = {{0167-6377}}, journal = {{Operations Research Letters}}, keywords = {{Applied Mathematics, Industrial and Manufacturing Engineering, Management Science and Operations Research, Software}}, number = {{3}}, pages = {{220--225}}, publisher = {{Elsevier BV}}, title = {{{Online load balancing on uniform machines with limited migration}}}, doi = {{10.1016/j.orl.2023.02.013}}, volume = {{51}}, year = {{2023}}, } @article{45757, abstract = {{AbstractThree prominent low order implicit time integration schemes are the first order implicit Euler-method, the second order trapezoidal rule and the second order Ellsiepen method. Its advantages are stability and comparatively low computational cost, however, they require the solution of a nonlinear system of equations. This paper presents a general approach for the construction of third order Runge–Kutta methods by embedding the above mentioned implicit schemes into the class of ELDIRK-methods. These will be defined to have an Explicit Last stage in the general Butcher array of Diagonal Implicit Runge–Kutta (DIRK) methods, with the consequence, that no additional system of equations must be solved. The main results—valid also for non-linear ordinary differential equations—are as follows: Two extra function calculations are required in order to embed the implicit Euler-method and one extra function calculation is required for the trapezoidal-rule and the Ellsiepen method, in order to obtain the third order properties, respectively. Two numerical examples are concerned with a parachute with viscous damping and a two-dimensional laser beam simulation. Here, we verify the higher order convergence behaviours of the proposed new ELDIRK-methods, and its successful performances for asymptotically exact global error estimation of so-called reversed embedded RK-method are shown. }}, author = {{Mahnken, Rolf}}, issn = {{0178-7675}}, journal = {{Computational Mechanics}}, keywords = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation}}}, doi = {{10.1007/s00466-023-02347-2}}, year = {{2023}}, } @article{46100, author = {{Hinrichs, Benjamin and Janssen, Daan W. and Ziebell, Jobst}}, issn = {{0022-247X}}, journal = {{Journal of Mathematical Analysis and Applications}}, keywords = {{Applied Mathematics, Analysis}}, number = {{1}}, publisher = {{Elsevier BV}}, title = {{{Super-Gaussian decay of exponentials: A sufficient condition}}}, doi = {{10.1016/j.jmaa.2023.127558}}, volume = {{528}}, year = {{2023}}, } @article{44081, author = {{Serino, Laura and Gil López, Jano and Stefszky, Michael and Ricken, Raimund and Eigner, Christof and Brecht, Benjamin and Silberhorn, Christine}}, issn = {{2691-3399}}, journal = {{PRX Quantum}}, keywords = {{General Physics and Astronomy, Mathematical Physics, Applied Mathematics, Electronic, Optical and Magnetic Materials, Electrical and Electronic Engineering, General Computer Science}}, number = {{2}}, publisher = {{American Physical Society (APS)}}, title = {{{Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States}}}, doi = {{10.1103/prxquantum.4.020306}}, volume = {{4}}, year = {{2023}}, } @article{53338, abstract = {{AbstractWe give an overview of analytical results concerned with chemotaxis systems where the signal is absorbed. We recall results on existence and properties of solutions for the prototypical chemotaxis‐consumption model and various variants and review more recent findings on its ability to support the emergence of spatial structures.}}, author = {{Lankeit, Johannes and Winkler, Michael}}, issn = {{0022-2526}}, journal = {{Studies in Applied Mathematics}}, keywords = {{Applied Mathematics}}, number = {{4}}, pages = {{1197--1229}}, publisher = {{Wiley}}, title = {{{Depleting the signal: Analysis of chemotaxis‐consumption models—A survey}}}, doi = {{10.1111/sapm.12625}}, volume = {{151}}, year = {{2023}}, } @article{30861, abstract = {{AbstractWe consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or Fuller phenomenon, which is problematic for applications. To avoid chattering, we introduce a reduced model which is still biologically relevant and retains the important structural features of the original problem. Using a combination of analytical and numerical methods, we show that the singular arc is dominant in the studied DOCPs and exhibits the turnpike property. This property is further used in order to design simple and realistic suboptimal control strategies.}}, author = {{Caillau, Jean-Baptiste and Djema, Walid and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}}, issn = {{0022-3239}}, journal = {{Journal of Optimization Theory and Applications}}, keywords = {{Applied Mathematics, Management Science and Operations Research, Control and Optimization}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Turnpike Property in Optimal Microbial Metabolite Production}}}, doi = {{10.1007/s10957-022-02023-0}}, year = {{2022}}, } @article{31479, author = {{Baswana, Surender and Gupta, Shiv and Knollmann, Till}}, issn = {{0178-4617}}, journal = {{Algorithmica}}, keywords = {{Applied Mathematics, Computer Science Applications, General Computer Science}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Mincut Sensitivity Data Structures for the Insertion of an Edge}}}, doi = {{10.1007/s00453-022-00978-0}}, year = {{2022}}, } @article{33264, abstract = {{We investigate bifurcations in feedforward coupled cell networks. Feedforward structure (the absence of feedback) can be defined by a partial order on the cells. We use this property to study generic one-parameter steady state bifurcations for such networks. Branching solutions and their asymptotics are described in terms of Taylor coefficients of the internal dynamics. They can be determined via an algorithm that only exploits the network structure. Similar to previous results on feedforward chains, we observe amplifications of the growth rates of steady state branches induced by the feedforward structure. However, contrary to these earlier results, as the interaction scenarios can be more complicated in general feedforward networks, different branching patterns and different amplifications can occur for different regions in the space of Taylor coefficients.}}, author = {{von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}}, issn = {{0951-7715}}, journal = {{Nonlinearity}}, keywords = {{Applied Mathematics, General Physics and Astronomy, Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{4}}, pages = {{2073--2120}}, publisher = {{IOP Publishing}}, title = {{{Amplified steady state bifurcations in feedforward networks}}}, doi = {{10.1088/1361-6544/ac5463}}, volume = {{35}}, year = {{2022}}, } @article{35306, author = {{Guedes Bonthonneau, Yannick and Weich, Tobias}}, issn = {{1435-9855}}, journal = {{Journal of the European Mathematical Society}}, keywords = {{Applied Mathematics, General Mathematics}}, number = {{3}}, pages = {{851--923}}, publisher = {{European Mathematical Society - EMS - Publishing House GmbH}}, title = {{{Ruelle–Pollicott resonances for manifolds with hyperbolic cusps}}}, doi = {{10.4171/jems/1103}}, volume = {{24}}, year = {{2022}}, } @article{34633, author = {{Hesse, Kerstin and Le Gia, Quoc Thong}}, issn = {{0377-0427}}, journal = {{Journal of Computational and Applied Mathematics}}, keywords = {{Applied Mathematics, Computational Mathematics}}, publisher = {{Elsevier BV}}, title = {{{L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data}}}, doi = {{10.1016/j.cam.2022.114118}}, volume = {{408}}, year = {{2022}}, } @article{47562, author = {{Herrmann, Felix and Grünewald, Marcus and Meijer, Tobias and Gardemann, Ulrich and Feierabend, Lukas and Riese, Julia}}, issn = {{0009-2509}}, journal = {{Chemical Engineering Science}}, keywords = {{Applied Mathematics, Industrial and Manufacturing Engineering, General Chemical Engineering, General Chemistry}}, publisher = {{Elsevier BV}}, title = {{{Operating window and flexibility of a lab-scale methanation plant}}}, doi = {{10.1016/j.ces.2022.117632}}, volume = {{254}}, year = {{2022}}, } @article{45970, abstract = {{ We introduce a new phase field model for tumor growth where viscoelastic effects are taken into account. The model is derived from basic thermodynamical principles and consists of a convected Cahn–Hilliard equation with source terms for the tumor cells and a convected reaction–diffusion equation with boundary supply for the nutrient. Chemotactic terms, which are essential for the invasive behavior of tumors, are taken into account. The model is completed by a viscoelastic system consisting of the Navier–Stokes equation for the hydrodynamic quantities, and a general constitutive equation with stress relaxation for the left Cauchy–Green tensor associated with the elastic part of the total mechanical response of the viscoelastic material. For a specific choice of the elastic energy density and with an additional dissipative term accounting for stress diffusion, we prove existence of global-in-time weak solutions of the viscoelastic model for tumor growth in two space dimensions [Formula: see text] by the passage to the limit in a fully-discrete finite element scheme where a CFL condition, i.e. [Formula: see text], is required. Moreover, in arbitrary dimensions [Formula: see text], we show stability and existence of solutions for the fully-discrete finite element scheme, where positive definiteness of the discrete Cauchy–Green tensor is proved with a regularization technique that was first introduced by Barrett and Boyaval [Existence and approximation of a (regularized) Oldroyd-B model, Math. Models Methods Appl. Sci. 21 (2011) 1783–1837]. After that, we improve the regularity results in arbitrary dimensions [Formula: see text] and in two dimensions [Formula: see text], where a CFL condition is required. Then, in two dimensions [Formula: see text], we pass to the limit in the discretization parameters and show that subsequences of discrete solutions converge to a global-in-time weak solution. Finally, we present numerical results in two dimensions [Formula: see text]. }}, author = {{Garcke, Harald and Kovács, Balázs and Trautwein, Dennis}}, issn = {{0218-2025}}, journal = {{Mathematical Models and Methods in Applied Sciences}}, keywords = {{Applied Mathematics, Modeling and Simulation}}, number = {{13}}, pages = {{2673--2758}}, publisher = {{World Scientific Pub Co Pte Ltd}}, title = {{{Viscoelastic Cahn–Hilliard models for tumor growth}}}, doi = {{10.1142/s0218202522500634}}, volume = {{32}}, year = {{2022}}, }