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

Universidad del Bío-Bío
Universidade Federal de Pernambuco

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

6 Scopus citations

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

Keywords

Coupled parabolic system
Lebesgue spaces
Local existence

Access to Document

10.1016/j.jde.2019.09.049

Cite this

@article{6f787cc1eb76437782742726afe8ef3a,

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{\texttimes}(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){\texttimes}Ls(Ω), u0,v0≥0, r,s∈[1,∞).",

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

author = "Aldryn Aparcana and Ricardo Castillo and Omar Guzm{\'a}n-Rea and Miguel Loayza",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2020",

month = mar,

day = "5",

doi = "10.1016/j.jde.2019.09.049",

language = "Ingl{\'e}s",

volume = "268",

pages = "3129--3151",

journal = "Journal of Differential Equations",

issn = "0022-0396",

number = "6",

}

TY - JOUR

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

UR - https://www.scopus.com/pages/publications/85072749093

U2 - 10.1016/j.jde.2019.09.049

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

Keywords

Access to Document

Other files and links

Fingerprint

Cite this