Estimates of the stabilization rate as t{yields}{infinity} of solutions of the first mixed problem for a quasilinear system of second-order parabolic equations

Journal Article · Mon Feb 28 00:00:00 EST 2000 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2000V191N02ABEH000454; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21202910

Kozhevnikova, L M ^[1]; Mukminov, F Kh ^[2]

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1. Sterlitamak State Pedagogical Institute, Sterlitamak (Russian Federation)
2. Bashkir State University, Ufa (Russian Federation)

A quasilinear system of parabolic equations with energy inequality is considered in a cylindrical domain {l_brace}t>0{r_brace}x{omega}. In a broad class of unbounded domains {omega} two geometric characteristics of a domain are identified which determine the rate of convergence to zero as t{yields}{infinity} of the L{sub 2}-norm of a solution. Under additional assumptions on the coefficients of the quasilinear system estimates of the derivatives and uniform estimates of the solution are obtained; they are proved to be best possible in the order of convergence to zero in the case of one semilinear equation.

• OSTI ID: 21202910
• Journal Information: Sbornik. Mathematics, Vol. 191, Issue 2; Other Information: DOI: 10.1070/SM2000v191n02ABEH000454; 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
CONVERGENCE
CYLINDRICAL CONFIGURATION
EQUATIONS
MATHEMATICAL SOLUTIONS
STABILIZATION