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Existence of solution for a class of heat equation in whole $ \mathbb{R}^N $

  • * Corresponding author: Tahir Boudjeriou

    * Corresponding author: Tahir Boudjeriou

C. O. Alves was partially supported by CNPq/Brazil 304804/2017-7

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  • In this paper we study the local and global existence of solutions for a class of heat equation in whole $ \mathbb{R}^{N} $ where the nonlinearity has a critical growth for $ N \geq 2 $. In order to prove the global existence, we will use the potential well theory combined with the Nehari manifold, and also with the Pohozaev manifold that is a novelty for this type of problem. Moreover, the blow-up phenomena of local solutions is investigated by combining the subdifferential approach with the concavity method.

    Mathematics Subject Classification: 35K60, 34B10, 35J15.

    Citation:

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