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<p>This paper deals with a nonlinear parabolic equation involving <i>p</i>(<i>x</i>)-Laplacian and nonstandard growth conditions, subject to a homogeneous Dirichlet boundary condition. In the critical initial energy case, we obtain the sharp condition on the existence of global and non-global solutions. We improve the blow-up criteria of solutions in the super critical initial energy case. The results complete the classification of the existence of global and blow-up solutions in the subcritical and critical initial energy cases respectively in Nhan (Nonlinear Anal. Real World Appl. 56:103155, 2020). Moreover, we obtain extinction or non-extinction phenomena of solutions through proving some energy estimate and an auxiliary lemma on some ODE.</p>

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Critical initial energy to a p(x)-Laplace equation with nonstandard growth conditions

  • 期刊论文

  • 发表日期：

    2025年11月27日

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  • Xizheng Sun

摘要

This paper deals with a nonlinear parabolic equation involving p(x)-Laplacian and nonstandard growth conditions, subject to a homogeneous Dirichlet boundary condition. In the critical initial energy case, we obtain the sharp condition on the existence of global and non-global solutions. We improve the blow-up criteria of solutions in the super critical initial energy case. The results complete the classification of the existence of global and blow-up solutions in the subcritical and critical initial energy cases respectively in Nhan (Nonlinear Anal. Real World Appl. 56:103155, 2020). Moreover, we obtain extinction or non-extinction phenomena of solutions through proving some energy estimate and an auxiliary lemma on some ODE.