Geodesic
Existence of global solutions and blow-up results for a class of p(x)−Laplacian Heat equations with logarithmic nonlinearity
Filomat, Tome 37 (2023) no. 22, p. 7527

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DOI

This paper's main objective is to examine an initial boundary value problem of a quasilinear parabolic equation of non-standard growth and logarithmic nonlinearity by utilizing the logarithmic Sobolev inequality and potential well method. Results of global existence, estimates of polynomial decay, and blowing up of weak solutions have been obtained under certain conditions that will be stated later. Our results extend those of a recent paper that appeared in the literature.
DOI : 10.2298/FIL2322527L
Classification : 35A01, 35B44, 35K55, 35K92
Keywords: Global existence, Blow-up, Potential well, Logarithmic source term, variable exponents 
Abdellatif Lalmi; Sarra Toualbia; Yamina Laskri. Existence of global solutions and blow-up results for a class of p(x)−Laplacian Heat equations with logarithmic nonlinearity. Filomat, Tome 37 (2023) no. 22, p. 7527 . doi: 10.2298/FIL2322527L
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     author = {Abdellatif Lalmi and Sarra Toualbia and Yamina Laskri},
     title = {Existence of global solutions and blow-up results for a class of {p(x)\ensuremath{-}Laplacian} {Heat} equations with logarithmic nonlinearity},
     journal = {Filomat},
     pages = {7527 },
     year = {2023},
     volume = {37},
     number = {22},
     doi = {10.2298/FIL2322527L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2322527L/}
}
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