A pseudoparabolic equation with nonlocal pu(x,t)$p\left[u(x,t)\right]$ ‐ Laplace operator

Abstract We study the Dirichlet problem for the pseudoparabolic equation perturbed with the ‐Laplacian diffusion term, where the argument of the exponent depends on the sought solution: with a given function . Under suitable conditions on the problem data, we prove the existence and uniqueness of a weak solution. It is shown that the solutions of the pseudoparabolic problem converge to the solution of the corresponding parabolic problem as .