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<p>In this paper, we have taken into account a model that incorporates two memory integrals with weak memory kernel and is delimited by a boundary consisting of Dirichlet boundary and no-flux boundary. We prove the existence of the global attractor and obtain conditions for the global stability of trivial steady-state via constructing the Lyapunov functional. Subsequently, the stability of the trivial steady-state solutions and associated bifurcation for this model are extensively investigated. It turns out that, for small parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mu\)</EquationSource> </InlineEquation>, the solutions of the equation will exhibit various dynamical behaviors when the parameters <i>R</i> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\lambda\)</EquationSource> </InlineEquation> are altered. For the inhomogeneous steady-state solution bifurcated from the trivial solution, we also provided the conditions for its stability and instability.</p>

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Bifurcation Analysis of a Heat Conduction Equation with Memory Effect

  • 期刊论文

  • 发表日期：

    2026年7月3日

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  • Jialiang Zhang,
  • Dejun Fan,
  • Chuncheng Wang,
  • Nikita Begun

摘要

In this paper, we have taken into account a model that incorporates two memory integrals with weak memory kernel and is delimited by a boundary consisting of Dirichlet boundary and no-flux boundary. We prove the existence of the global attractor and obtain conditions for the global stability of trivial steady-state via constructing the Lyapunov functional. Subsequently, the stability of the trivial steady-state solutions and associated bifurcation for this model are extensively investigated. It turns out that, for small parameter \(\mu\) , the solutions of the equation will exhibit various dynamical behaviors when the parameters R and \(\lambda\) are altered. For the inhomogeneous steady-state solution bifurcated from the trivial solution, we also provided the conditions for its stability and instability.