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Applied Math Seminar: Extension of Kreiss theory for hyperbolic problems to surface and glancing waves

Event Type: 
Seminar
Speaker: 
Mohammad Motamed
Event Date: 
Monday, November 3, 2014 - 10:00am
Location: 
SMLC 356
Audience: 
General PublicFaculty/StaffStudentsAlumni/Friends

Event Description: 

Abstract: The Kreiss symmetrizer technique gives sharp estimates of the solution of the first order hyperbolic initial-boundary value problems both in the interior and on the boundary of the domain. Such estimates imply a strongly well-posed problem. The best reference is the book by H.-O. Kreiss and J. Lorenz "Initial-boundary value problems and the Navier-Stokes equations, SIAM, 2004."

There are however problems which are not strongly well-posed but are well-posed in a weaker sense, i.e., problems for which sharp estimates of the solution can be obtained only in the interior and not on the boundary. These types of problems are important in elastic and electromagnetic wave propagation when boundary phenomena, such as surface and glancing waves, occur. We introduce a new concept of well-posedness and extend the Kreiss theory to study such problems. Both first-order and second-order systems of hyperbolic problems in multi-spatial dimension will be considered. The importance of the developed analysis is that it can be used, by introducing discrete norms, to study numerical stability of finite difference schemes for such problems.

Event Contact

Contact Name: Daniel Appelo

Contact Email: appelo@math.unm.edu