The exixtence of generalized solutions for a class of linear and nonlinear equations of mixed type

Abstract

In this paper we deal with the question of existence and uniqueness of the generalized solutions for a class of linear and nonlinear equations of the mixed type. In particular we consider in a simply connected region G , where for and for . G is bounded by the curves Γ₀,Γ₁,Γ₂.Γ₀y > 0y= 0P(- 1,0)Q(0,0)Γ₁y < (Error rendering LaTeX formula)Γ_{2(Error rendering LaTeX formula)Γ1$ either lies in the characteristic triangle formed by the characteristics through P and Q (Frankl Problem) or coincides with the characteristics through P (Tricomi Problem). We seek sufficient conditions for the existence and uniqueness of generalized solutions of the boundary problem (Error rendering LaTeX formula)}