Existence and regularity theorems for a two-phase degenerate stefan problem with convection

Abstract

A domain D in the (z, y) pla.ne is surrounded by curves OA, OB a.nd a line segment AB (a part of a s-traight line x = 0 > 0). For t,he following initmid-boundary value problem of the La.pla.ce hyperbolic differential inequality some results on maximum properties of Sathe? are irnyrwed in this paper, smoothness and monotonicity hypotheses in Sathera imposed on the initial curve OA and the boundary cnnre OB are relaxed, a class of strong maximum principles is established and uniqueness of solutions of the initial-boundary value. problem is prcnrecl.

Keywords:

• Strong maximum principle,
• Laplace hyperbolic equation
• initial-boundary value problem