On the mixed problem for quasilinear pseudoparabolic equation

Abstract

In this paper the multidimensional mixed problem for the quasilinear pseudoparabolic equation u_t-L_xu-εL_xu_t=f(t,x,u) is considered. L_x is a differential operator, which composes (with boundary operator) a self adjoint operator. An existence, uniqueness and also continuous dependense on the small parameter ε>0 of generalized solution is proved. The estimation of the difference of exact and approximate solutions is obtained

Keywords:

• Quasilinear pseudoparabolic equation
• mixed problem
• system of nonlinear integral equations
• generalized solutions