Existence and stability of solutions to nonlocal parabolic problems with variable exponent
Abdelilah Lamrani Alaoui, Ahmed Jamea, Abderrahmane El Hachimi · AIP conference proceedings · 2019
We are studying a nonlinear nonlocal Dirichlet parabolic problem associated with the following p(x)−laplacian equation ∂u∂t−a(∫Ω| ∇u |p(x)p(x))Δp(x)u=f(x,t) We apply Galerkin’s approximation technique, some uniform estimates and a compactness arguments to prove the existence result. Then we investigate the uniqueness of solutions, finally we give an answer to the asymptotic behavior question.