Boundary value problems for first-order mixed complex equations with degenerate curve

Abstract

This article deals with some boundary value problems for quasilinear mixed (elliptic-hyperbolic) complex equations of first order with degenerate hyperbolic curve in a simply connected domain. First, we give the representation theorem and prove the uniqueness of solutions for the above boundary value problems. Then using the method of successive iteration, the existence of solutions for the above problems is proved.

Keywords:

• boundary value problems
• quasilinear mixed complex equations
• degenerate hyperbolic curve

AMS Subject Classifications:

• 35M05
• 35J70
• 35L80

Acknowledgement

This research is supported by the NSFC (No. 10971224).