Asymptotic behaviour of solutions of the first boundary-value problem for strongly hyperbolic systems near a conical point at the boundary of the domain

Journal Article · Tue Aug 31 00:00:00 EDT 1999 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM1999V190N07ABEH000415; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21202876

Hung, Nguyen M ^[1]

---

1. M.V. Lomonosov Moscow State University, Moscow (Russian Federation)

An existence and uniqueness theorem for generalized solutions of the first initial-boundary-value problem for strongly hyperbolic systems in bounded domains is established. The question of estimates in Sobolev spaces of the derivatives with respect to time of the generalized solution is discussed. It is shown that the smoothness of generalized solutions with respect to time is independent of the structure of the boundary of the domain but depends on the coefficients of the right-hand side. Results on the smoothness of the generalized solution and its asymptotic behaviour in a neighbourhood of a conical boundary point are also obtained.

• OSTI ID: 21202876
• Journal Information: Sbornik. Mathematics, Vol. 190, Issue 7; Other Information: DOI: 10.1070/SM1999v190n07ABEH000415; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
BOUNDARY-VALUE PROBLEMS
MATHEMATICAL SPACE
SMOOTH MANIFOLDS