On the existence, uniqueness and stability of solutions for semi-linear generalized elasticity equation with general damping term
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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.
KeywordsGeneralized semi-linear elasticity equation nonlinear internal stabilization generalized Lebesgue space Sobolev spaces with variable exponents
MR(2010) Subject Classification58J45 35L53 35L71 46E30 46E35
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We thank the referees for their time and comments.
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