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<p>This article is devoted to the existence and blow-up of solutions the semi-linear parabolic equation with singular potential function and nonlinear Neumann boundary condition on cone Sobolev spaces. More precise, we obtained a threshold result for the global existence of solution and proved the existence time of solution is finite when the initial energy satisfies certain condition.</p>

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Nonlinear Neumann problem with a singular potential function on the manifold with conical singularity

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Yasser Khalili,
  • Morteza Koozehgar Kalleji

摘要

This article is devoted to the existence and blow-up of solutions the semi-linear parabolic equation with singular potential function and nonlinear Neumann boundary condition on cone Sobolev spaces. More precise, we obtained a threshold result for the global existence of solution and proved the existence time of solution is finite when the initial energy satisfies certain condition.