Decay rate estimates for a new class of multidimensional nonlinear Bresse systems with time-dependent dissipations


This paper studies the existence of weak solutions and their asymptotic behaviour to the initial boundary value problem for a multidimensional nonlinear Bresse system. The existence of the solutions of the problem is obtained by appliying Galerkin method. Then, we obtain an explicit decay rate estimation dependent on both the strain-caused stress and the damping terms by using the multiplier method with integral.

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This work was supported by the Directorate-General for Scientific Research and Technological Development (DGRSDT) (Algeria). The author would like to thank the editor and the referees for their very helpful suggestions.

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Correspondence to Hanni Dridi.

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Dridi, H. Decay rate estimates for a new class of multidimensional nonlinear Bresse systems with time-dependent dissipations. Ricerche mat (2021).

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  • Multidimensional Bresse system
  • Nonlinear systems
  • Stability
  • Arch problems, damping terms
  • Galerkin method
  • Multiplier technique

Mathematics Subject Classification

  • 35B40
  • 45K05
  • 74D05
  • 74D99