FOURIER METHOD FOR A QUASILINEAR PARABOLIC EQUATION WITH PERIODIC BOUNDARY CONDITION

Abstract

A multidimensional mixed problem with Neuman type periodic boundary condition is studied for the quasilinear parabolic equation ∂u∂t −a2 ∂2u∂x2 = f(t, x, u). The existence, uniqueness and also continuity ofthe weak generalized solution is proved.