INTIAL BOUNDARY VALUE PROBLEM IN A HALF-SPACE WITH CONSTANT COEEFICIENTS
This chapter drops the assumption of symmetry, or at least it does not assume the dissipativity in a classical sense. The search for a necessary condition for maximal estimates (strong well-posedness in Kreiss' sense) yields the so-called uniform Kreiss-Lopatinskii condition. The chapter investigates the case of a characteristic boundary. It gives practical devices to check the K.-L. condition, including the construction of a Lopatinskii determinant. It shows that the adjoint BVP shares with the direct one the K.-L. condition, a fact exploited in the duality method employed in the existence theory. The latter is carried out for the BVP in weighted (in time) spaces under the assumption that a Kreiss' dissipative boundary symmetrizer exists. Its existence is stated for a constantly hyperbolic operator, but the proof will be seen in the next chapter. The evolutionary property is shown with the use of the Paley-Wiener Theorem. Rauch's Theorem tells what the solution at a given time T can be estimated to; this extends the well-posedness to the full IBVP.
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
If you think you should have access to this title, please contact your librarian.