Existence of solution and asymptotic behavior for a class of parabolic equations

Anderson L. A. de Araujo; Marcelo Montenegro

doi:10.3934/cpaa.2021017

Article Contents

2021, Volume 20, Issue 3: 1213-1227. Doi: 10.3934/cpaa.2021017

This issue Previous Article Cylindrical estimates for mean curvature flow in hyperbolic spaces Next Article Global well-posedness of the

$ n $

-dimensional hyper-dissipative Boussinesq system without thermal diffusivity

Existence of solution and asymptotic behavior for a class of parabolic equations

Anderson L. A. de Araujo^1, and
Marcelo Montenegro^2, ,

1.
Universidade Federal de Viçosa, Departamento de Matemática, Avenida Peter Henry Rolfs, s/n, CEP 36570-900, Viçosa, MG, Brasil
2.
Universidade Estadual de Campinas, IMECC, Departamento de Matemática, Rua Sérgio Buarque de Holanda, 651, CEP 13083-859, Campinas, SP, Brasil

^* Corresponding author
^* Corresponding author

Received: June 30, 2020

Revised: November 30, 2020

Early access: February 2021

Published: March 2021

The authors have been supported by FAPESP and CNPq

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Abstract

We prove existence and uniqueness of a positive solution for a class of quasilinear parabolic equations. We also show some maximum principles on the derivatives of the solution and study the asymptotic behavior of the solution near the maximal time of existence.

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Mathematics Subject Classification: Primary: 35K10, 35B50; Secondary: 35K90, 35K67.

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References

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