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Acta Mathematica Sinica, English Series

, Volume 33, Issue 11, pp 1549–1564 | Cite as

On the existence, uniqueness and stability of solutions for semi-linear generalized elasticity equation with general damping term

Article

Abstract

In this paper, we consider a semi-linear generalized hyperbolic boundary value problem associated to the linear elastic equations with general damping term and nonlinearities of variable exponent type. Under suitable conditions, local and global existence theorems are proved. The uniqueness of the solution have been gotten by eliminating some hypotheses that have been imposed by other authors for different particular problems. We show that any solution with nontrivial initial datum becomes stable.

Keywords

Generalized semi-linear elasticity equation nonlinear internal stabilization generalized Lebesgue space Sobolev spaces with variable exponents 

MR(2010) Subject Classification

58J45 35L53 35L71 46E30 46E35 

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Notes

Acknowledgements

We thank the referees for their time and comments.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Technical SciencesLaghouat UniversityLaghouatAlgeria

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