For partial differential equations of mixed elliptic-hyperbolic type we prove results on existence and existence with uniqueness of weak solutions for closed boundary value problems of Dirichlet and mixed Dirichlet-conormal types. These problems are of interest for applications to transonic flow and are over-determined for solutions with classical regularity. The method employed consists in variants of the a-b-c integral method of Friedrichs in Sobolev spaces with suitable weights. Particular attention is paid to the problem of attaining results with a minimum of restrictions on the boundary geometry and the form of the type change function. In addition, interior regularity results are also given in the important special case of the Tricomi equation.
|Titolo:||On closed boundary value problems for equations of mixed elliptic-hyperbolic type|
|Autori interni:||PAYNE, KEVIN RAY (Ultimo)|
|Parole Chiave:||existence ; uniqueness ; weak solution ; mixed type equation ; Dirichlet problem|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2007|
|Digital Object Identifier (DOI):||10.1002/cpa.20169|
|Appare nelle tipologie:||01 - Articolo su periodico|