Smooth solution of one boundary-value problem

Abstract

We study the boundary value problem for the quasilinear equation u _u − u_xx=F[u, u_t], u(x, 0)= u(x, π)=0, u(x+w, t)=u(x, t), x ε ®, t ε [0, π], and establish conditions under which a theorem on the uniqueness of a smooth solution is true.