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A Robin–Dirichlet problem for a nonlinear wave equation with the source term containing a nonlinear integral

Abstract

In this paper, we consider the Robin–Dirichlet problem for a nonlinear wave equation with the source term containing a nonlinear integral. Using the Faedo–Galerkin method and the linearization method for nonlinear terms, we prove the existence and uniqueness of a weak solution. We also discuss an asymptotic expansion of high order in a small parameter of a weak solution.

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Correspondence to Nguyen Huu Nhan.

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Nhan, N.H., Ngoc, L.T.P., Thuyet, T.M. et al. A Robin–Dirichlet problem for a nonlinear wave equation with the source term containing a nonlinear integral. Lith Math J 57, 80–108 (2017). https://doi.org/10.1007/s10986-017-9345-4

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MSC

  • 35L20
  • 35L70
  • 35Q72

Keywords

  • Faedo–Galerkinmethod
  • linear recurrent sequence
  • Robin–Dirichlet conditions
  • asymptotic expansion in many small parameters