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<p>We consider a class of blow-up solutions for perturbed nonlinear heat equations involving gradient terms. We first prove the single-point blow-up property for this equation and determine its final blow-up profile. We also give a sharper description of its blow-up behavior, where we take as a profile some suitably chosen solution of the unperturbed semilinear heat equation. The proof relies on selfsimilar variables with involved arguments to control the gradient term.</p>

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Non-explicit sharp profile for blow-up solutions of perturbed nonlinear heat equations with gradient terms

  • 期刊论文

  • 发表日期：

    2025年7月28日

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  • Maissâ Boughrara

摘要

We consider a class of blow-up solutions for perturbed nonlinear heat equations involving gradient terms. We first prove the single-point blow-up property for this equation and determine its final blow-up profile. We also give a sharper description of its blow-up behavior, where we take as a profile some suitably chosen solution of the unperturbed semilinear heat equation. The proof relies on selfsimilar variables with involved arguments to control the gradient term.