Parametrices, singularities, and high frequency asymptotics in the theory of sound waves
Part of the International Centre for Mechanical Sciences book series (CISM, volume 277)
Let Ω ≤ R3 be an unbounded domain with bounded complement and boundary ∂Ω ∈ C∞. Let with C1 ≤ a(x), b(x) ≤ C2 for x ∈ Ω and for suitable constants C1,C2 > 0. In the next section I want to study the singularities of solutions v(x,t) of the following Dirichlet and Neumann problems
where f, v0,v1 are given functions, and where ∂n denotes the derivative of v with respect to the normal n at the boundary ∂Ω × R+. To do this, I need results from the solution theory, and in particular, from the regularity theory of these problems. These results are well known and can be proved, for example, by semi-group theory. Therefore, in this introductory section I only give some definitions and state the results needed later on.
KeywordsWave Equation Neumann Problem Wave Operator Infinite Order Riemann Function
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© Springer-Verlag Wien 1983