Singularities of the Solutions of Non-Correct Mixed Problems for Second Order Strictly Hyperbolic Operators

✍ Scribed by Todor V. Gramchev; Peter R. Popivanov

• Publisher: John Wiley and Sons
• Year: 1985
• Tongue: English
• Weight: 433 KB
• Volume: 121
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19851210107

✦ Synopsis

S 1. Introduction and statement of the results

1. The full proofs of the results stated in [18] are given in this paper. We consider the mixed problem (or the init,ial boundary value problem) for a second order strictly hyperbolic operator with a singular oblique derivative. This is the case when the smooth vector field is tangent to the boundary at some points. As it concerns the case of a vector field nowhere tangent to the boundary many papers have been devotedsee for example [5], [6], [TI, [9], [ll]. A few papers deal with the singular oblique derivative case [12], [13].

In contrast with them we study the propagation of singularities and the Cm semi-correctness of the problem. In our papers [17], [19] we prove some necessary conditions for C" semi-correctness and propagation of singularities. We are interested here in mixed problems violating the necessary conditions mentioned above.