Existence and uniqueness of weak solutions to parabolic problems with nonstandard growth and cross diffusion
Date
2020-12-17
Authors
Arumugam, Gurusamy
Erhardt, Andre H.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We establish the existence and uniqueness of weak solutions to the parabolic system with nonstandard growth condition and cross diffusion,
∂tu - div α(x, t, ∇u)) = div |F|p(x,t)-2 F),
∂tv - div α(x, t, ∇v)) = δ∆u,
where δ ≥ 0 and ∂tu, ∂tv denote the partial derivative of u and v with respect to the time variable t, while ∇u and ∇v denote the one with respect to the spatial variable x. Moreover, the vector field α(x, t, ‧) satisfies certain nonstandard p(x, t) growth, monotonicity and coercivity conditions.
Description
Keywords
Nonlinear parabolic problem, Nonstandard growth, Cross diffusion
Citation
Arumugam, G., & Erhardt, A. H. (2020). Existence and uniqueness of weak solutions to parabolic problems with nonstandard growth and cross diffusion. <i>Electronic Journal of Differential Equations, 2020</i>(123), pp. 1-13.