@article{63337, abstract = {{AbstractIn boundedn-dimensional domainsΩ, the Neumann problem for the parabolic equation$$\begin{array}{} \displaystyle u_t = \nabla \cdot \Big( A(x,t)\cdot\nabla u\Big) + \nabla \cdot \Big(b(x,t)u\Big) - f(x,t,u)+g(x,t) \end{array}$$(*)is considered for sufficiently regular matrix-valuedA, vector-valuedband real valuedg, and withfrepresenting superlinear absorption in generalizing the prototypical choice given byf(⋅, ⋅,s) =sαwithα> 1. Problems of this form arise in a natural manner as sub-problems in several applications such as cross-diffusion systems either of Keller-Segel or of Shigesada-Kawasaki-Teramoto type in mathematical biology, and accordingly a natural space for initial data appears to beL1(Ω).The main objective thus consists in examining how far solutions can be constructed for initial data merely assumed to be integrable, with major challenges potentially resulting from the interplay between nonlinear degradation on the one hand, and the possibly destabilizing drift-type action on the other in such contexts. Especially, the applicability of well-established methods such as techniques relying on entropy-like structures available in some particular cases, for instance, seems quite limited in the present setting, as these typically rely on higher initial regularity properties.The first of the main results shows that in the general framework of (*), nevertheless certain global very weak solutions can be constructed through a limit process involving smooth solutions to approximate variants thereof, provided that the ingredients of the latter satisfy appropriate assumptions with regard to their stabilization behavior.The second and seemingly most substantial part of the paper develops a method by which it can be shown, under suitably stregthened hypotheses on the integrability ofband the degradation parameterα, that the solutions obtained above in fact form genuine weak solutions in a naturally defined sense. This is achieved by properly exploiting a weak integral inequality, as satisfied by the very weak solution at hand, through a testing procedure that appears to be novel and of potentially independent interest.To underline the strength of this approach, both these general results are thereafter applied to two specific cross-diffusion systems. Inter alia, this leads to a statement on global solvability in a logistic Keller-Segel system under the assumptionα>$\begin{array}{} \frac{2n+4}{n+4} \end{array}$on the respective degradation rate which seems substantially milder than any previously found condition in the literature. Apart from that, for a Shigesada-Kawasaki-Teramoto system some apparently first results on global solvability forL1initial data are derived.}}, author = {{Winkler, Michael}}, issn = {{2191-950X}}, journal = {{Advances in Nonlinear Analysis}}, number = {{1}}, pages = {{526--566}}, publisher = {{Walter de Gruyter GmbH}}, title = {{{The role of superlinear damping in the construction of solutions to drift-diffusion problems with initial data in L1}}}, doi = {{10.1515/anona-2020-0013}}, volume = {{9}}, year = {{2019}}, } @article{63334, author = {{Tao, Youshan and Winkler, Michael}}, issn = {{0022-0396}}, journal = {{Journal of Differential Equations}}, number = {{9}}, pages = {{4973--4997}}, publisher = {{Elsevier BV}}, title = {{{Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy}}}, doi = {{10.1016/j.jde.2019.10.046}}, volume = {{268}}, year = {{2019}}, } @article{63349, author = {{Bellomo, Nicola and Painter, Kevin J. and Tao, Youshan and Winkler, Michael}}, issn = {{0036-1399}}, journal = {{SIAM Journal on Applied Mathematics}}, number = {{5}}, pages = {{1990--2010}}, publisher = {{Society for Industrial & Applied Mathematics (SIAM)}}, title = {{{Occurrence vs. Absence of Taxis-Driven Instabilities in a May--Nowak Model for Virus Infection}}}, doi = {{10.1137/19m1250261}}, volume = {{79}}, year = {{2019}}, } @article{63350, author = {{Fila, Marek and Winkler, Michael}}, issn = {{0001-8708}}, journal = {{Advances in Mathematics}}, publisher = {{Elsevier BV}}, title = {{{A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation}}}, doi = {{10.1016/j.aim.2019.106823}}, volume = {{357}}, year = {{2019}}, } @article{63355, abstract = {{AbstractThis work studies the two‐species Shigesada–Kawasaki–Teramoto model with cross‐diffusion for one species, as given by with positive parameters and , and nonnegative constants and . Beyond some statements on global existence, the literature apparently provides only few results on qualitative behavior of solutions; in particular, questions related to boundedness as well as to large time asymptotics in seem unsolved so far.In the present paper it is inter alia shown that if and is a bounded convex domain with smooth boundary, then whenever and are nonnegative, the associated Neumann initial‐boundary value problem for possesses a global classical solution which in fact is bounded in the sense that Moreover, the asymptotic behavior of arbitrary nonnegative solutions enjoying the boundedness property is studied in the general situation when is arbitrary and no longer necessarily convex. If , then in both cases and , an explicit smallness condition on is identified as sufficient for stabilization of any nontrivial solutions toward a corresponding unique nontrivial spatially homogeneous steady state. If and , then without any further assumption all nonzero solutions are seen to approach the equilibrium (0,1). As a by‐product, this particularly improves previous knowledge on nonexistence of nonconstant equilibria of .}}, author = {{Tao, Youshan and Winkler, Michael}}, issn = {{0024-6115}}, journal = {{Proceedings of the London Mathematical Society}}, number = {{6}}, pages = {{1598--1632}}, publisher = {{Wiley}}, title = {{{Boundedness and stabilization in a population model with cross‐diffusion for one species}}}, doi = {{10.1112/plms.12276}}, volume = {{119}}, year = {{2019}}, } @article{63356, abstract = {{ This work deals with a taxis cascade model for food consumption in two populations, namely foragers directly orienting their movement upward the gradients of food concentration and exploiters taking a parasitic strategy in search of food via tracking higher forager densities. As a consequence, the dynamics of both populations are adapted to the space distribution of food which is dynamically modified in time and space by the two populations. This model extends the classical one-species chemotaxis-consumption systems by additionally accounting for a second taxis mechanism coupled to the first in a consecutive manner. It is rigorously proved that for all suitably regular initial data, an associated Neumann-type initial-boundary value problem for the spatially one-dimensional version of this model possesses a globally defined bounded classical solution. Moreover, it is asserted that the considered two populations will approach spatially homogeneous distributions in the large time limit, provided that either the total population number of foragers or that of exploiters is appropriately small. }}, author = {{Tao, Youshan and Winkler, Michael}}, issn = {{0218-2025}}, journal = {{Mathematical Models and Methods in Applied Sciences}}, number = {{11}}, pages = {{2151--2182}}, publisher = {{World Scientific Pub Co Pte Ltd}}, title = {{{Large time behavior in a forager–exploiter model with different taxis strategies for two groups in search of food}}}, doi = {{10.1142/s021820251950043x}}, volume = {{29}}, year = {{2019}}, } @article{63352, author = {{Lankeit, Johannes and Winkler, Michael}}, issn = {{0021-2172}}, journal = {{Israel Journal of Mathematics}}, number = {{1}}, pages = {{249--296}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Counterintuitive dependence of temporal asymptotics on initial decay in a nonlocal degenerate parabolic equation arising in game theory}}}, doi = {{10.1007/s11856-019-1900-8}}, volume = {{233}}, year = {{2019}}, } @article{63358, author = {{Tao, Youshan and Winkler, Michael}}, issn = {{1553-5258}}, journal = {{Communications on Pure & Applied Analysis}}, number = {{4}}, pages = {{2047--2067}}, publisher = {{American Institute of Mathematical Sciences (AIMS)}}, title = {{{A chemotaxis-haptotaxis system with haptoattractant remodeling: Boundedness enforced by mild saturation of signal production}}}, doi = {{10.3934/cpaa.2019092}}, volume = {{18}}, year = {{2019}}, } @article{63357, author = {{Tao, Youshan and Winkler, Michael}}, issn = {{0022-0396}}, journal = {{Journal of Differential Equations}}, number = {{1}}, pages = {{388--406}}, publisher = {{Elsevier BV}}, title = {{{Global smooth solvability of a parabolic–elliptic nutrient taxis system in domains of arbitrary dimension}}}, doi = {{10.1016/j.jde.2019.01.014}}, volume = {{267}}, year = {{2019}}, } @article{63353, author = {{Lankeit, Johannes and Winkler, Michael}}, issn = {{0012-0456}}, journal = {{Jahresbericht der Deutschen Mathematiker-Vereinigung}}, number = {{1}}, pages = {{35--64}}, publisher = {{Springer Fachmedien Wiesbaden GmbH}}, title = {{{Facing Low Regularity in Chemotaxis Systems}}}, doi = {{10.1365/s13291-019-00210-z}}, volume = {{122}}, year = {{2019}}, } @article{63351, author = {{Krzyżanowski, Piotr and Winkler, Michael and Wrzosek, Dariusz}}, issn = {{1468-1218}}, journal = {{Nonlinear Analysis: Real World Applications}}, pages = {{94--116}}, publisher = {{Elsevier BV}}, title = {{{Migration-driven benefit in a two-species nutrient taxis system}}}, doi = {{10.1016/j.nonrwa.2019.01.006}}, volume = {{48}}, year = {{2019}}, } @article{63362, abstract = {{The system \left\{\begin{matrix} u_{t} = \mathrm{\Delta }u−\chi \mathrm{∇} \cdot \left(\frac{u}{v}\mathrm{∇}v\right)−uv + B_{1}(x,t), \\ v_{t} = \mathrm{\Delta }v + uv−v + B_{2}(x,t), \\ \end{matrix}\right.\:\:( \star ) is considered in a disk \mathrm{\Omega } \subset \mathbb{R}^{2} , with a positive parameter χ and given nonnegative and suitably regular functions B_{1} and B_{2} defined on \mathrm{\Omega } \times (0,\infty ) . In the particular version obtained when \chi = 2 , ( \star ) was proposed in [31] as a model for crime propagation in urban regions. Within a suitable generalized framework, it is shown that under mild assumptions on the parameter functions and the initial data the no-flux initial-boundary value problem for ( \star ) possesses at least one global solution in the case when all model ingredients are radially symmetric with respect to the center of Ω . Moreover, under an additional hypothesis on stabilization of the given external source terms in both equations, these solutions are shown to approach the solution of an elliptic boundary value problem in an appropriate sense. The analysis is based on deriving a priori estimates for a family of approximate problems, in a first step achieving some spatially global but weak initial regularity information which in a series of spatially localized arguments is thereafter successively improved. To the best of our knowledge, this is the first result on global existence of solutions to the two-dimensional version of the full original system ( \star ) for arbitrarily large values of χ . }}, author = {{Winkler, Michael}}, issn = {{0294-1449}}, journal = {{Annales de l'Institut Henri Poincaré C, Analyse non linéaire}}, number = {{6}}, pages = {{1747--1790}}, publisher = {{European Mathematical Society - EMS - Publishing House GmbH}}, title = {{{Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation}}}, doi = {{10.1016/j.anihpc.2019.02.004}}, volume = {{36}}, year = {{2019}}, } @article{63363, abstract = {{ This work is concerned with a prototypical model for the spatio-temporal evolution of a forager–exploiter system, consisting of two species which simultaneously consume a common nutrient, and which interact through a taxis-type mechanism according to which individuals from the exploiter subpopulation move upward density gradients of the forager subgroup. Specifically, the model [Formula: see text] for the population densities [Formula: see text] and [Formula: see text] of foragers and exploiters, as well as the nutrient concentration [Formula: see text], is considered in smoothly bounded domains [Formula: see text], [Formula: see text]. It is first shown that under an explicit condition linking the sizes of the resource production rate [Formula: see text] and of the initial nutrient concentration, an associated Neumann-type initial-boundary value problem admits a global solution within an appropriate generalized concept. The second of the main results asserts stabilization of these solutions toward spatially homogeneous equilibria in the large time limit, provided that [Formula: see text] satisfies a mild assumption on temporal decay. To the best of our knowledge, these are the first rigorous analytical results addressing taxis-type cross-diffusion mechanisms coupled in a cascade-like manner as in (⋆). }}, author = {{Winkler, Michael}}, issn = {{0218-2025}}, journal = {{Mathematical Models and Methods in Applied Sciences}}, number = {{03}}, pages = {{373--418}}, publisher = {{World Scientific Pub Co Pte Ltd}}, title = {{{Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions}}}, doi = {{10.1142/s021820251950012x}}, volume = {{29}}, year = {{2019}}, } @article{63366, author = {{Winkler, Michael}}, issn = {{0362-546X}}, journal = {{Nonlinear Analysis}}, pages = {{102--116}}, publisher = {{Elsevier BV}}, title = {{{Instantaneous regularization of distributions from(C0)⋆×L2in the one-dimensional parabolic Keller–Segel system}}}, doi = {{10.1016/j.na.2019.01.017}}, volume = {{183}}, year = {{2019}}, } @article{63359, author = {{Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}}, issn = {{0944-2669}}, journal = {{Calculus of Variations and Partial Differential Equations}}, number = {{6}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{The fast signal diffusion limit in Keller–Segel(-fluid) systems}}}, doi = {{10.1007/s00526-019-1656-3}}, volume = {{58}}, year = {{2019}}, } @article{63364, author = {{Winkler, Michael}}, issn = {{0373-3114}}, journal = {{Annali di Matematica Pura ed Applicata (1923 -)}}, number = {{5}}, pages = {{1615--1637}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{How strong singularities can be regularized by logistic degradation in the Keller–Segel system?}}}, doi = {{10.1007/s10231-019-00834-z}}, volume = {{198}}, year = {{2019}}, } @article{63367, author = {{Winkler, Michael}}, issn = {{1021-9722}}, journal = {{Nonlinear Differential Equations and Applications NoDEA}}, number = {{6}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Does repulsion-type directional preference in chemotactic migration continue to regularize Keller–Segel systems when coupled to the Navier–Stokes equations?}}}, doi = {{10.1007/s00030-019-0600-8}}, volume = {{26}}, year = {{2019}}, } @misc{8482, author = {{Jurgelucks, Benjamin and Schulze, Veronika and Feldmann, Nadine and Claes, Leander}}, title = {{{Arbitrary sensitivity for inverse problems in piezoelectricity}}}, year = {{2019}}, } @inproceedings{12952, author = {{Dreiling, Dmitrij and Feldmann, Nadine and Henning, Bernd}}, keywords = {{piezoelectric materials, piezoelectric properties, DC bias field, non-linear material parameters}}, location = {{Nürnberg}}, publisher = {{AMA Service GmbH}}, title = {{{A DC bias approach to the characterisation of non-linear material parameters of piezoelectric ceramics}}}, doi = {{10.5162/sensoren2019/5.1.2}}, year = {{2019}}, } @article{59495, author = {{Güsken, Nicholas Alexander and Lauri, Alberto and Li, Yi and Matsui, Takayuki and Doiron, Brock and Bower, Ryan and Regoutz, Anna and Mihai, Andrei and Petrov, Peter K. and Oulton, Rupert F. and Cohen, Lesley F. and Maier, Stefan A.}}, issn = {{2330-4022}}, journal = {{ACS Photonics}}, number = {{4}}, pages = {{953--960}}, publisher = {{American Chemical Society (ACS)}}, title = {{{TiO2–x-Enhanced IR Hot Carrier Based Photodetection in Metal Thin Film–Si Junctions}}}, doi = {{10.1021/acsphotonics.8b01639}}, volume = {{6}}, year = {{2019}}, }