Global Existence and Blow-Up of Solutions to a Parabolic Nonlocal Equation Arising in a Theory of Thermal Explosion
Focusing on the physical context of the thermal explosion model, this paper investigates a semilinear parabolic equation ut=Δu+a∫Ωupdx,x,t∈QT,n·∇u+guu=0,x,t∈ST,ux,0=u0x,x∈Ω with nonlocal sources under nonlinear heat-loss boundary conditions, where a,p>0 is constant, QT=Ω×0,T, ST=∂Ω×0,T, and Ω is...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/4629799 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832554737120051200 |
|---|---|
| author | Wenyuan Ma Zhixuan Zhao Baoqiang Yan |
| author_facet | Wenyuan Ma Zhixuan Zhao Baoqiang Yan |
| author_sort | Wenyuan Ma |
| collection | DOAJ |
| description | Focusing on the physical context of the thermal explosion model, this paper investigates a semilinear parabolic equation ut=Δu+a∫Ωupdx,x,t∈QT,n·∇u+guu=0,x,t∈ST,ux,0=u0x,x∈Ω with nonlocal sources under nonlinear heat-loss boundary conditions, where a,p>0 is constant, QT=Ω×0,T, ST=∂Ω×0,T, and Ω is a bounded region in RN,N≥1 with a smooth boundary ∂Ω. First, we prove a comparison principle for some kinds of semilinear parabolic equations under nonlinear boundary conditions; using it, we show a new theorem of subsupersolutions. Secondly, based on the new method of subsupersolutions, the existence of global solutions and blow-up solutions is presented for different values of p. Finally, the blow-up rate for solutions is estimated also. |
| format | Article |
| id | doaj-art-da75b0e6b3e948539146a69215318982 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-da75b0e6b3e948539146a692153189822025-02-03T05:50:41ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/4629799Global Existence and Blow-Up of Solutions to a Parabolic Nonlocal Equation Arising in a Theory of Thermal ExplosionWenyuan Ma0Zhixuan Zhao1Baoqiang Yan2School of Mathematics and StatisticsSchool of Mathematics and StatisticsSchool of Mathematics and StatisticsFocusing on the physical context of the thermal explosion model, this paper investigates a semilinear parabolic equation ut=Δu+a∫Ωupdx,x,t∈QT,n·∇u+guu=0,x,t∈ST,ux,0=u0x,x∈Ω with nonlocal sources under nonlinear heat-loss boundary conditions, where a,p>0 is constant, QT=Ω×0,T, ST=∂Ω×0,T, and Ω is a bounded region in RN,N≥1 with a smooth boundary ∂Ω. First, we prove a comparison principle for some kinds of semilinear parabolic equations under nonlinear boundary conditions; using it, we show a new theorem of subsupersolutions. Secondly, based on the new method of subsupersolutions, the existence of global solutions and blow-up solutions is presented for different values of p. Finally, the blow-up rate for solutions is estimated also.http://dx.doi.org/10.1155/2022/4629799 |
| spellingShingle | Wenyuan Ma Zhixuan Zhao Baoqiang Yan Global Existence and Blow-Up of Solutions to a Parabolic Nonlocal Equation Arising in a Theory of Thermal Explosion Journal of Function Spaces |
| title | Global Existence and Blow-Up of Solutions to a Parabolic Nonlocal Equation Arising in a Theory of Thermal Explosion |
| title_full | Global Existence and Blow-Up of Solutions to a Parabolic Nonlocal Equation Arising in a Theory of Thermal Explosion |
| title_fullStr | Global Existence and Blow-Up of Solutions to a Parabolic Nonlocal Equation Arising in a Theory of Thermal Explosion |
| title_full_unstemmed | Global Existence and Blow-Up of Solutions to a Parabolic Nonlocal Equation Arising in a Theory of Thermal Explosion |
| title_short | Global Existence and Blow-Up of Solutions to a Parabolic Nonlocal Equation Arising in a Theory of Thermal Explosion |
| title_sort | global existence and blow up of solutions to a parabolic nonlocal equation arising in a theory of thermal explosion |
| url | http://dx.doi.org/10.1155/2022/4629799 |
| work_keys_str_mv | AT wenyuanma globalexistenceandblowupofsolutionstoaparabolicnonlocalequationarisinginatheoryofthermalexplosion AT zhixuanzhao globalexistenceandblowupofsolutionstoaparabolicnonlocalequationarisinginatheoryofthermalexplosion AT baoqiangyan globalexistenceandblowupofsolutionstoaparabolicnonlocalequationarisinginatheoryofthermalexplosion |