Semilinear Hyperbolic Boundary Value Problem Associated to the Nonlinear Generalized Viscoelastic Equations

Abstract

Consider a semilinear hyperbolic boundary value problem associated to the nonlinear generalized viscoelastic equations with Direchlet-Neumann boundary conditions. Then, the global existence of a weak solution is established. The uniqueness of the solution has been obtained by eliminating some hypotheses that have been imposed by other authors for different particular problems.

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Correspondence to Abita Rahmoune.

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Rahmoune, A. Semilinear Hyperbolic Boundary Value Problem Associated to the Nonlinear Generalized Viscoelastic Equations. Acta Math Vietnam 43, 219–238 (2018). https://doi.org/10.1007/s40306-017-0229-9

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Keywords

  • Global existence
  • General damped
  • Nonlinear viscoelastic
  • Generalized Lebesgue space
  • Sobolev spaces with variable exponents
  • Memory term

Mathematics Subject Classification (2010)

  • 35L75
  • 35B40
  • 35L15
  • 35L70
  • 35B40
  • 35A01
  • 76A10