Fourier method for a quasilinear pseudo-parabolic equation with periodic boundary condition

Abstract

A multidimensional mixed problem with Neuman type periodic boundary condition is studied for quasilinear pseudo-parabolic equation ?u/?ta2 ?2u/?x2 - ? ?3u/?t?x2 = f(t, x, u). The existence, uniqueness and also convergence of the weak generalized solution is proved. © 2009 Academic Publications.