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Article Dans Une Revue Journal of Differential Equations Année : 2021

Construction of a blow-up solution for a perturbed nonlinear heat equation with a gradient term

Résumé

We consider in this paper a perturbation of the standard semilinear heat equation by a term involving the space derivative and a non-local term. We prove the existence of a blow-up solution, and give its blow-up profile. Our method relies on the two-step method: we first linearize the equation (in similarity variables) around the expected profile, then we use a topological argument to controle the positive directions of the spectrum.

Dates et versions

hal-02370323 , version 1 (19-11-2019)

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Citer

Bouthaina Abdelhedi, Hatem Zaag. Construction of a blow-up solution for a perturbed nonlinear heat equation with a gradient term. Journal of Differential Equations, 2021, 272, pp.1-45. ⟨10.1016/j.jde.2020.09.020⟩. ⟨hal-02370323⟩
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