Weak well-posedness for the Dirichlet problem for equations of mixed elliptic-hyperbolic type
Other Research Product
Publication Date:
2005
Citation:
Weak well-posedness for the Dirichlet problem for equations of mixed elliptic-hyperbolic type / K.R. Payne. ((Intervento presentato al convegno Equazioni a derivate parziali: aspetti metodologici, modellistica, applicazioni tenutosi a Ragusa Ibla nel giugno 2005.
abstract:
Equations of mixed elliptic-hyperbolic type with a homogeneous Dirichlet condition imposed on the entire boundary will be
discussed. Such closed problems are typically overdetermined
in spaces of classical solutions in contrast to the well-posedness for classical solutions that can result from opening the
boundary by prescribing the boundary condition only on a proper subset of the boundary. Closed problems arise, for example, in models of transonic fluid flow about a given profile, but very little is known on the well-posedness in spaces of weak solutions. We present recent progress, obtained in collaboration with D. Lupo and C. S. Morawetz, on the well-posedness in weighted Sobolev spaces as well as the beginnings of a regularity theory.
discussed. Such closed problems are typically overdetermined
in spaces of classical solutions in contrast to the well-posedness for classical solutions that can result from opening the
boundary by prescribing the boundary condition only on a proper subset of the boundary. Closed problems arise, for example, in models of transonic fluid flow about a given profile, but very little is known on the well-posedness in spaces of weak solutions. We present recent progress, obtained in collaboration with D. Lupo and C. S. Morawetz, on the well-posedness in weighted Sobolev spaces as well as the beginnings of a regularity theory.
IRIS type:
14 - Intervento a convegno non pubblicato
Keywords:
Solvability, overdertermined problems, multiplier methods, a priori estimates
List of contributors:
K.R. Payne
Link to information sheet: