UNIQUENESS THEOREMS FOR A NONLINEAR TRICOMI PROBLEM AND THE RELATED EVOLUTION PROBLEM

We consider an initial-boundary value problem for the non-linear evolution equation GRAPHICS in a cylinder Q(t)=Omega x (0, t), where T u =yu(xx) + u(yy) is the Tricomi operator and l(u) a special differential operator of first order. In 10 we proved the existence of a generalized solution of problem (1) and the existence of a generalized solution of the corresponding stationary boundary value problem (non-linear Tricomi problem) L(T) u =T u + r(x,y)u\u\(rho) = f(x,y,u) in Omega. In this paper we give sufficient conditions for the uniqueness of these solutions.