Local well‐posedness and blow‐up for an inhomogeneous nonlinear heat equation | Zendy

Alessa Rasha | Zendy; Alshehri Aisha | Zendy; Altamimi Haya | Zendy; Majdoub Mohamed | Zendy

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Local well‐posedness and blow‐up for an inhomogeneous nonlinear heat equation

Author(s) -

Alessa Rasha,

Alshehri Aisha,

Altamimi Haya,

Majdoub Mohamed

Publication year - 2020

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.6266

Subject(s) - mathematics , nonlinear system , standard probability space , lebesgue integration , heat equation , polynomial , mathematical analysis , exponential growth , space (punctuation) , lp space , exponential function , function (biology) , banach space , linguistics , philosophy , physics , quantum mechanics , evolutionary biology , biology

In this paper, we consider the nonlinear heat equation with inhomogeneous nonlinearityu t − Δ u = a ( x ) f ( u ) where f : R → R having either a polynomial growth or exponential growth, and a : R N → R is a function satisfying some assumptions to be stated later. We first prove the local well‐posedness in suitable Lebesgue spaces when a belongs to some Lebesgue space and f has polynomial growth. We also obtain some blow‐up results.

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