New approach to prove the existence of classical solutions for a class of nonlinear parabolic equations
Georgiev, Svetlin G. ; Zennir, Khaled
CUBO, A Mathematical Journal, Tome 20 (2018), / Harvested from Cubo, A Mathematical Journal
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In this article, we consider a class of nonlinear parabolic equations. We use an integral representation combined with a sort of fixed point theorem to prove the existence of classical solutions for the initial value problem (1.1), (1.2). We also obtain a result on continuous dependence on the initial data. We propose a new approach for investigation for existence of classical solutions of some classes nonlinear parabolic equations.

Publié le : 2018-07-01
DOI : https://doi.org/10.4067/S0719-06462018000200023 
@article{2048,
     title = {New approach to prove the existence of classical solutions for a class of nonlinear parabolic equations},
     journal = {CUBO, A Mathematical Journal},
     volume = {20},
     year = {2018},
     doi = {10.4067/S0719-06462018000200023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/2048}
}

Georgiev, Svetlin G.; Zennir, Khaled. New approach to prove the existence of classical solutions for a class of nonlinear parabolic equations. CUBO, A Mathematical Journal, Tome 20 (2018) . doi : 10.4067/S0719-06462018000200023. http://gdmltest.u-ga.fr/item/2048/