ASYMPTOTIC PROPERTIES FOR A SEMILINEAR PLATE EQUATION IN UNBOUNDED DOMAINS-Reference-Cited by-同舟云学术

ASYMPTOTIC PROPERTIES FOR A SEMILINEAR PLATE EQUATION IN UNBOUNDED DOMAINS

Published:2009-06 Issue:02 Volume:06 Page:269-294
ISSN:0219-8916
Container-title:Journal of Hyperbolic Differential Equations
language:en
Short-container-title:J. Hyper. Differential Equations

Author:

DA LUZ CLEVERSON ROBERTO¹,CHARÃO RUY COIMBRA²

Affiliation:

1. Institute of Mathematics, Federal University of Rio de Janeiro, Cidade Universitária, Campus do Fundão, 21945-970 Rio de Janeiro RJ, Brazil

2. Department of Mathematics, Federal University of Santa Catarina, Campus Universitário, Trindade, 88040-900 Florianópolis SC, Brazil

Abstract

We study the existence, uniqueness, and asymptotic properties of global solutions to the initial value problem associated with a semilinear, dissipative, plate equation under rotational inertia effects in ℝn. We obtain polynomial decay rate in time for the total energy. In dimension n ≥ 5 for the linear problem and n = 5 for the semilinear problem with small data, we obtain fast decay of the total energy and a decay rate t-1/2 for L2-norm of the solution and similar decay rates for the L2-norm of higher-order derivatives.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219891609001824

Reference29 articles.

1. Mathematics;Adams R. A.,1975

2. Energy decay rates for the Timoshenko system of thermoelastic plates

3. Decay of solutions for a semilinear system of elastic waves in an exterior domain with damping near infinity

4. A justification of the von Kármán equations

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