Existence and uniqueness of weak solutions to parabolic problems with nonstandard growth and cross diffusion
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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.
CitationArumugam, G., & Erhardt, A. H. (2020). Existence and uniqueness of weak solutions to parabolic problems with nonstandard growth and cross diffusion. Electronic Journal of Differential Equations, 2020(123), pp. 1-13.
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