New approach to prove the existence of classical solutions for a class of nonlinear parabolic equations

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DOI:

https://doi.org/10.4067/S0719-06462018000200023

Abstract

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.

Keywords

parabolic equation , existence , differentiability with respect to the initial data
  • Svetlin G. Georgiev Department of Differential Equations, Faculty of Mathematics and Informatics, University of Sofia, Sorbonne University, Paris, France.
  • Khaled Zennir Department of Mathematics, College of Sciences and Arts, Al-Ras. Qassim University, Kingdom Of Saudi Arabia.
  • Pages: 23–39
  • Date Published: 2018-07-31
  • Vol. 20 No. 2 (2018)

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Published

2018-07-31

How to Cite

[1]
S. G. Georgiev and K. Zennir, “New approach to prove the existence of classical solutions for a class of nonlinear parabolic equations”, CUBO, vol. 20, no. 2, pp. 23–39, Jul. 2018.

Issue

Vol. 20 No. 2 (2018)

Section

Articles