On the local existence for a weakly parabolic system in Lebesgue spaces

Aldryn Aparcana; Ricardo Castillo; Omar Guzmán-Rea; Miguel Loayza

doi:10.1016/j.jde.2019.09.049

On the local existence for a weakly parabolic system in Lebesgue spaces

Aldryn Aparcana, Ricardo Castillo, Omar Guzmán-Rea, Miguel Loayza

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Abstract

We consider the parabolic system u_t−aΔu=f(v),v_t−bΔv=g(u) in Ω×(0,T), where a,b>0, f,g:[0,∞)→[0,∞) are non-decreasing continuous functions and either Ω is a bounded domain with smooth boundary ∂Ω or the whole space R^N. We characterize the functions f and g so that the system has a local solution for every initial data (u₀,v₀)∈L^r(Ω)×L^s(Ω), u₀,v₀≥0, r,s∈[1,∞).

Original language	English
Pages (from-to)	3129-3151
Number of pages	23
Journal	Journal of Differential Equations
Volume	268
Issue number	6
DOIs	https://doi.org/10.1016/j.jde.2019.09.049
State	Published - 5 Mar 2020

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

Coupled parabolic system
Lebesgue spaces
Local existence

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10.1016/j.jde.2019.09.049

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title = "On the local existence for a weakly parabolic system in Lebesgue spaces",

abstract = "We consider the parabolic system ut−aΔu=f(v),vt−bΔv=g(u) in Ω×(0,T), where a,b>0, f,g:[0,∞)→[0,∞) are non-decreasing continuous functions and either Ω is a bounded domain with smooth boundary ∂Ω or the whole space RN. We characterize the functions f and g so that the system has a local solution for every initial data (u0,v0)∈Lr(Ω)×Ls(Ω), u0,v0≥0, r,s∈[1,∞).",

keywords = "Coupled parabolic system, Lebesgue spaces, Local existence",

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T1 - On the local existence for a weakly parabolic system in Lebesgue spaces

AU - Aparcana, Aldryn

AU - Castillo, Ricardo

AU - Guzmán-Rea, Omar

AU - Loayza, Miguel

PY - 2020/3/5

Y1 - 2020/3/5

N2 - We consider the parabolic system ut−aΔu=f(v),vt−bΔv=g(u) in Ω×(0,T), where a,b>0, f,g:[0,∞)→[0,∞) are non-decreasing continuous functions and either Ω is a bounded domain with smooth boundary ∂Ω or the whole space RN. We characterize the functions f and g so that the system has a local solution for every initial data (u0,v0)∈Lr(Ω)×Ls(Ω), u0,v0≥0, r,s∈[1,∞).

AB - We consider the parabolic system ut−aΔu=f(v),vt−bΔv=g(u) in Ω×(0,T), where a,b>0, f,g:[0,∞)→[0,∞) are non-decreasing continuous functions and either Ω is a bounded domain with smooth boundary ∂Ω or the whole space RN. We characterize the functions f and g so that the system has a local solution for every initial data (u0,v0)∈Lr(Ω)×Ls(Ω), u0,v0≥0, r,s∈[1,∞).

KW - Coupled parabolic system

KW - Lebesgue spaces

KW - Local existence

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DO - 10.1016/j.jde.2019.09.049

M3 - Artículo

AN - SCOPUS:85072749093

SN - 0022-0396

VL - 268

SP - 3129

EP - 3151

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 6

ER -

On the local existence for a weakly parabolic system in Lebesgue spaces

Abstract

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Keywords

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