Abstract:

We studied the first initial and boundary value problems for a class of pseudoparabolic equations with variable exponent in a smooth domain Ω. Firstly, we constructed the approximate solutions through Galerkin method, then under some conditions limited on the parameter, using energy method, we obtained the uniform estimates for the approximate solutions. At last, using the above estimate, we gave the existence and uniqueness result for the original
 problem.

Key words: pseudoparabolic equations, variable exponent, existence and uniqueness