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PDE of mixed type: well posedness and spectral theory for linear boundary value problems

Giovedi' 17 Febbraio 2011 - Kevin Payne

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Giovedi' 17 febbraio 2011 alle ore 11:00 in sala riunioni VII piano Kevin Payne (Universita' di Milano) terra' un seminario dal titolo "PDE of mixed type: well posedness and spectral theory for linear boundary value problems".

-Abstract
Partial Differential Equations (PDE) of mixed elliptic-hyperbolic type arise in particular but interesting contexts such as transonic fluid flow and isometric embeddings of Riemannian manifolds whose curvature changes sign. Problems which involve mixed type PDE are difficult as the mixture of qualitative types competes with the fact that sharp PDE tools are often calibrated to the type of the equation. The most interesting and natural problems involve, of course, nonlinear equations, but progress on them remains inhibited due to a glaring lack of precise information on linear equations of mixed type. In particular, what constitutes a well posed boundary value problem and what can one say about spectral theory? We will give a general overview of some of the interesting problems which involve mixed type PDE as well as progress towards an adequate solvability and spectral theory for linear boundary value problems. The results to be presented are part of an ongoing collaboration with Daniela Lupo (Politecnico di Milano), Dario Monticelli (Universita' di Milano) and Cathleen Morawetz (Courant Institute-NYU).

Rif. int. M. Bardi, P. Mannucci, C. Marchi

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