Gurusamy Arumugam, Andre H. Erhardt
We establish the existence and uniqueness of weak solutions to the parabolic system with nonstandard growth condition and cross diffusion,
where and denote the partial derivative of u and v with respect to the time variable t, while and denote the one with respect to the spatial variable x. Moreover, the vector field 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.
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| Gurusamy Arumugam |
Discipline of Mathematics
Indian Institute of Technology Gandhinagar
Gandhinagar, 382355 Gujarat, India
email: email@example.com, firstname.lastname@example.org
| André H. Erhardt |
Department of Mathematics
University of Oslo, P.O. Box 1053 Blindern
N-0316 Oslo, Norway
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