On a Class of Nonlinear Viscoelastic Kirchhoff Plates: Well-Posedness and General Decay Rates

Journal Article · Mon Feb 15 00:00:00 EST 2016 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-015-9298-0· OSTI ID:22722833

Silva, M. A. Jorge, ^[1]; Rivera, J. E. Muñoz, ^[2]

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1. State University of Londrina, Department of Mathematics (Brazil)
2. National Laboratory of Scientific Computation (Brazil)

This paper is concerned with well-posedness and energy decay rates to a class of nonlinear viscoelastic Kirchhoff plates. The problem corresponds to a class of fourth order viscoelastic equations of p-Laplacian type which is not locally Lipschitz. The only damping effect is given by the memory component. We show that no additional damping is needed to obtain uniqueness in the presence of rotational forces. Then, we show that the general rates of energy decay are similar to ones given by the memory kernel, but generally not with the same speed, mainly when we consider the nonlinear problem with large initial data.

• OSTI ID: 22722833
• Journal Information: Applied Mathematics and Optimization, Vol. 73, Issue 1; Other Information: Copyright (c) 2016 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BENDING
DAMPING
DECAY
ELASTICITY
EQUATIONS
KERNELS
LAPLACIAN
NONLINEAR PROBLEMS
PLATES
VISCOSITY