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

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

Aníbal RodrÍguez-Bernal
, Alejandro Vidal-López

Universidad Complutense de Madrid
University of Warwick

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	635-644
Number of pages	10
Journal	Communications on Pure and Applied Analysis
Volume	13
Issue number	2
DOIs	https://doi.org/10.3934/cpaa.2014.13.635
Publication status	Published - Mar 2014
Externally published	Yes

Keywords

Asymptotic behavior
Critical exponents
Global existence
Reaction-diffusion
Singular initial data
Strong solutions

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10.3934/cpaa.2014.13.635

Cite this

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

abstract = "We show existence and uniqueness of global solutions for reaction- diffusion equations with almost-monotonic nonlinear terms in L q(Ω) for each 1 ≤ q < ∞. In particular, we do not assume restriction on the growth of the nonlinearites required by the standar local existence theory.",

keywords = "Asymptotic behavior, Critical exponents, Global existence, Reaction-diffusion, Singular initial data, Strong solutions",

author = "An{\'i}bal Rodr{\'I}guez-Bernal and Alejandro Vidal-L{\'o}pez",

year = "2014",

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AU - RodrÍguez-Bernal, Aníbal

AU - Vidal-López, Alejandro

PY - 2014/3

Y1 - 2014/3

N2 - We show existence and uniqueness of global solutions for reaction- diffusion equations with almost-monotonic nonlinear terms in L q(Ω) for each 1 ≤ q < ∞. In particular, we do not assume restriction on the growth of the nonlinearites required by the standar local existence theory.

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

KW - Asymptotic behavior

KW - Critical exponents

KW - Global existence

KW - Reaction-diffusion

KW - Singular initial data

KW - Strong solutions

UR - https://www.scopus.com/pages/publications/84888139578

U2 - 10.3934/cpaa.2014.13.635

DO - 10.3934/cpaa.2014.13.635

M3 - Article

AN - SCOPUS:84888139578

SN - 1534-0392

VL - 13

SP - 635

EP - 644

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 2

ER -

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

Abstract

Keywords

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