A note on the existence  of global solutions for reaction-diffusion equations with almost-monotonic  nonlinearities

Aníbal Rodríguez-Bernal; Alejandro Vidal-López

doi:10.3934/cpaa.2014.13.635

Article Contents

2014, Volume 13, Issue 2: 635-644. Doi: 10.3934/cpaa.2014.13.635

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A note on the existence of global solutions for reaction-diffusion equations with almost-monotonic nonlinearities

Aníbal Rodríguez-Bernal^1, and
Alejandro Vidal-López^2,

1.
Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid 28040
2.
Mathematics Institute, University of Warwick, Coventry, CV4 7AL

Received: December 31, 2012

Revised: August 31, 2013

Published: February 2014

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Abstract

We show existence and uniqueness of global solutions for reaction-diffusion equations with almost-monotonic nonlinear terms in $L^q(\Omega)$ for each $1\leq q < \infty$. In particular, we do not assume restriction on the growth of the nonlinearites required by the standar local existence theory.

Keywords:

Mathematics Subject Classification: Primary: 35A01, 35B33, 35D35, 35K57, 35K20; Secondary: 35B40, 35B41.

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References

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