TY  - JOUR
A1  - Yin, H. C.
A1  - Witt, Ingo
T1  - Global singularity structure of weak solutions to 3-D semilinear dispersive wave equations with discontinuous initial data
N2  - 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
Y1  - 2004
SN  - 0022-0396
ER  - 
TY  - JOUR
A1  - Liu, Xiaochun
A1  - Witt, Ingo
T1  - Pseudodifferential calculi on the half-line respecting prescribed asymptotic types
N2  - Given asymptotics types P, Q, pseudodifferential operators A is an element of L-cl(mu) (R+) are constructed in such a way that if u(t) possesses conormal asymptotics of type P as t --> +0, then Au(t) possesses conormal asymptotics of type Q as t --> +0. This is achieved by choosing the operators A in Schulze's cone algebra on the half-line R+, controlling their complete Mellin symbols {sigma(M)(u-j) (A); j is an element of N}, and prescribing the mapping properties of the residual Green operators. The constructions lead to a coordinate invariant calculus, including trace and potential operators at t = 0, in which a parametrix construction for the elliptic elements is possible. Boutet de Monvel's calculus for pseudodifferential boundary problems occurs as a special case when P = Q is the type resulting from Taylor expansion at t = 0.
Y1  - 2004
SN  - 0378-620X
ER  - 
TY  - JOUR
A1  - Witt, Ingo
T1  - Local asymptotic types
N2  - The local theory of asymptotic types is elaborated. It appears as coordinate-free version of part of GOHBERG- SIGAL'S theory of the inversion of finitely meromorphic, operator-valued functions at a point
Y1  - 2004
SN  - 0025-2611
ER  - 
TY  - JOUR
A1  - Dreher, M
A1  - Witt, Ingo
T1  - Energy estimates for weakly hyperbolic systems of the first order
N2  - 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
Y1  - 2005
ER  -