Boundary value problems for nonlinear differential equations of mixed - composite type in R³

Abstract

In bounded simply connected regions G with G n {x₃ ≡ 0} ≠ Φ boundary value problems are studied for nonlinear equations of the form

with , where T is the Tricomi operator and a,b,c,d are given functions of (x₁,x₂,x₃)∈G. We prove the existence of generalized solutions by using apriori estimates for certain boundary value problems for the corresponding linear equation Lu ≡ g(x₁,x₂,x₃). These estimates ensure the solvability of finite dimensional nonlinear equations related to (0); their solutions approximate in a specified sense the generalized solution of (0)

AMS(MOS)::

• 35MO5
• 35G15
• 35G30
• 35B45
• 35D05