Existence of solutions for a nonlinear system of parabolic equations with gradient flow structure

DOI10.1007/s00605-013-0573-3zbMath1302.35202OpenAlexW2092176029MaRDI QIDQ403832

Jonathan Zinsl

Publication date: 29 August 2014

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-013-0573-3

zbMATH Keywords

Wasserstein metricdegenerate diffusionglobal weak solutionKeller-Segel systemtime-discrete solution

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Degenerate parabolic equations (35K65) Initial value problems for second-order parabolic systems (35K45) Cell movement (chemotaxis, etc.) (92C17) Quasilinear parabolic equations (35K59)

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Existence of solutions for a class of fourth order cross-diffusion systems of gradient flow type ⋮ High-frequency limit of non-autonomous gradient flows of functionals with time-periodic forcing ⋮ Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure ⋮ Incompressible immiscible multiphase flows in porous media: a variational approach ⋮ A Wasserstein gradient flow approach to Poisson−Nernst−Planck equations ⋮ A note on the variational analysis of the parabolic-parabolic Keller-Segel system in one spatial dimension ⋮ Self-Similarity in a Thin Film Muskat Problem ⋮ Well-posedness of evolution equations with time-dependent nonlinear mobility: a modified minimizing movement scheme ⋮ Exponential convergence to equilibrium in a Poisson-Nernst-Planck-type system with nonlinear diffusion

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