Conditions for the Existence of Global Solutions to Doubly Nonlinear Advection-diffusion Equations

Authors

DOI:

https://doi.org/10.5540/tema.2020.021.01.83

Keywords:

Doubly nonlinear parabolic equation, global solutions, conditions for global solutions

Abstract

 In this work, we consider a initial-value problem for an doubly non linear advection-diffusion equation, and we present a critical value of κ up to wich the initial-value problem has global solution independent of the initial data u0, and from which global solutions may still exists, but from initial data u0 satisfying certain conditions. For this, we suppose that the function f(x,t,u) in the advection term, writted in the divergent form, satisfies certain conditions about your variation in Rn, and we also use the decrease of the norm L1(Rn) and an control for the norm L∞(Rn) of solution u(·,t). 

Author Biographies

Jocemar Q. Chagas, UEPG - Universidade Estadual de Ponta Grossa

Departamento de Matemática e Estatística

Patrícia L. Guidolin, UFRGS - Universidade Federal do Rio Grande do Sul

Departamento de Matemática Pura e Aplicada

Paulo R. Zingano, UFRGS - Universidade Federal do Rio Grande do Sul

Departamento de Matemática Pura e Aplicada

References

References

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J. Q. Chagas, P. L. Guidolin, and P. R. Zingano, Norma do sup para equações de advecção-difusão duplamente não lineares: o caso geral, in Proceeding Series of the Brazilian Society of Applied and Computational Mathematics, no. 7, SBMAC, 2018. (Pré-print).

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Published

2020-03-27

How to Cite

Chagas, J. Q., Guidolin, P. L., & Zingano, P. R. (2020). Conditions for the Existence of Global Solutions to Doubly Nonlinear Advection-diffusion Equations. Trends in Computational and Applied Mathematics, 21(1), 83. https://doi.org/10.5540/tema.2020.021.01.83

Issue

Vol. 21 No. 1 (2020)

Section

Original Article

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