Refine
Has Fulltext
- no (17)
Document Type
- Monograph/Edited Volume (12)
- Article (4)
- Doctoral Thesis (1)
Is part of the Bibliography
- yes (17) (remove)
Institute
Asymptotic algebras
(2001)
For a class of first-order weakly hyperbolic pseudo-differential systems with finite time degeneracy, well- posedness of the Cauchy problem is proved in an adapted scale of Sobolev spaces. These Sobolev spaces are constructed in correspondence to the hyperbolic operator under consideration, making use of ideas from the theory of elliptic boundary value problems on manifolds with singularities. In addition, an upper bound for the loss of regularity that occurs when passing from the Cauchy data to the solutions is established. In many examples, this upper bound turns out to be sharp
We study the global singularity structure of solutions to 3-D semilinear wave equations with discontinuous initial data. More precisely, using Strichartz' inequality we show that the solutions stay conormal after nonlinear interaction if the Cauchy data are conormal along a circle. (C) 2003 Elsevier Inc. All rights reserved