Existence of regular solutions to a class of parabolic systems in two space dimensions with critical growth behaviour

DOI10.1007/s11565-009-0071-7zbMath1205.35145OpenAlexW2042011438MaRDI QIDQ626985

Jens Frehse, Maria Specovius-Neugebauer

Publication date: 19 February 2011

Published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11565-009-0071-7

zbMATH Keywords

Hölder continuityglobal solutionsnonlinear parabolic systems

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear parabolic equations (35K55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quasilinear parabolic equations (35K59) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (10)

Parabolic systems with quadratic nonlinearities in the gradient. Regularity of solutions ⋮ Regular and irregular solutions for a class of elliptic systems in the critical dimension ⋮ Global existence of weak solutions to a Keller-Segel model with \(L^1\) initial data ⋮ Global solvability of the Cauchy-Dirichlet problem for a class of strongly nonlinear parabolic systems ⋮ \(L^\infty\) a priori bounds for gradients of solutions to quasilinear inhomogeneous fast-growing parabolic systems ⋮ Local regularity of weak solutions to a class of parabolic systems with quadratic nonlinearities in the gradient ⋮ Regularity conditions for nonlinear elliptic systems with quadratic nonlinearities in the gradient ⋮ Weak global solvability of the two-phase problem for a class of parabolic systems with strong nonlinearity in the gradient. The case of two spatial variables ⋮ ON NONLINEAR ELLIPTIC BELLMAN SYSTEMS FOR A CLASS OF STOCHASTIC DIFFERENTIAL GAMES IN ARBITRARY DIMENSION ⋮ Heat flow for a class of quadratic functionals with nondiagonal principal matrix. Existence of a smooth global solution

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