Arumugam, GurusamyGurusamyArumugamErhardt, André H.André H.Erhardt2025-08-312025-08-312020-01-012-s2.0-85098890544https://d8.irins.org/handle/IITG2025/25708We establish the existence and uniqueness of weak solutions to the parabolic system with nonstandard growth condition and cross diffusion, ∂<inf>t</inf>u − div a(x, t, ∇u)) = div |F |^p(x,t)−2F ), ∂<inf>t</inf>v − div a(x, t, ∇v)) = δ∆u, where δ ≥ 0 and ∂<inf>t</inf>u, ∂<inf>t</inf>v 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 a(x, t, ·) satisfies certain nonstandard p(x, t) growth, monotonicity and coercivity conditions.falseCross diffusion | Nonlinear parabolic problem | Nonstandard growthArticle107266911-1320201123arJournal