Electron. J. Differential Equations, Vol. 2020 (2020), No. 123, pp. 1-13.

Existence and uniqueness of weak solutions to parabolic problems with nonstandard growth and cross diffusion

Gurusamy Arumugam, Andre H. Erhardt

Abstract:
We establish the existence and uniqueness of weak solutions to the parabolic system with nonstandard growth condition and cross diffusion,

where $\delta\ge0$ and $\partial_tu,~\partial_tv$ denote the partial derivative of u and v with respect to the time variable t, while $\nabla u$ and $\nabla v$ denote the one with respect to the spatial variable x. Moreover, the vector field $a(x,t,\cdot)$ satisfies certain nonstandard p(x,t) growth, monotonicity and coercivity conditions.

Submitted September 18, 2019. Published December 17, 2020.
Math Subject Classifications: 35A01, 35D30, 35K65.
Key Words: Nonlinear parabolic problem; nonstandard growth; cross diffusion.
DOI: 10.58997/ejde.2020.123

Show me the PDF file (367 KB), TEX file for this article.

Gurusamy Arumugam
Discipline of Mathematics
Indian Institute of Technology Gandhinagar
Gandhinagar, 382355 Gujarat, India
email: gurusamy.a@iitgn.ac.in, guru.poy@gmail.com
André H. Erhardt
Department of Mathematics
University of Oslo, P.O. Box 1053 Blindern
N-0316 Oslo, Norway
email: andreerh@math.uio.no

Return to the EJDE web page