Global Existence and Uniform Blow-Up to a Nonlocal Parabolic System with Nonlinear Boundary Conditions Arising in a Thermal Explosion Theory
This paper deals with a nonlinear nonlocal parabolic system with nonlinear heat-loss boundary conditions, which arise in the thermal explosion model. Firstly, we prove a comparison principle for some kinds of parabolic systems under nonlinear boundary conditions. Using this, we improve a new theorem...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI
2023
|
| Subjects: | |
| Online Access: | View Fulltext in Publisher View in Scopus |
| LEADER | 01609nam a2200205Ia 4500 | ||
|---|---|---|---|
| 001 | 10.3390-math11091993 | ||
| 008 | 230529s2023 CNT 000 0 und d | ||
| 020 | |a 22277390 (ISSN) | ||
| 245 | 1 | 0 | |a Global Existence and Uniform Blow-Up to a Nonlocal Parabolic System with Nonlinear Boundary Conditions Arising in a Thermal Explosion Theory |
| 260 | 0 | |b MDPI |c 2023 | |
| 856 | |z View Fulltext in Publisher |u https://doi.org/10.3390/math11091993 | ||
| 856 | |z View in Scopus |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-85159213980&doi=10.3390%2fmath11091993&partnerID=40&md5=c167b31216c9d4befe6a4c2bd4db3046 | ||
| 520 | 3 | |a This paper deals with a nonlinear nonlocal parabolic system with nonlinear heat-loss boundary conditions, which arise in the thermal explosion model. Firstly, we prove a comparison principle for some kinds of parabolic systems under nonlinear boundary conditions. Using this, we improve a new theorem of the sub-and-super solution. Secondly, based on the new sub-and-super solution theorem, the sufficient conditions that the solution exists and blows up uniformly in finite time are presented. Then, we generalize some of the lemmas related to uniform blow-up solutions, which are used to introduce the uniform blow-up profiles of solutions. Finally, we give several numerical simulations to illustrate the existence and uniform blow-up of solutions. © 2023 by the authors. | |
| 650 | 0 | 4 | |a blow-up profile |
| 650 | 0 | 4 | |a global existence |
| 650 | 0 | 4 | |a nonlinear boundary conditions |
| 650 | 0 | 4 | |a nonlocal sources |
| 700 | 1 | 0 | |a Ma, W. |e author |
| 700 | 1 | 0 | |a Yan, B. |e author |
| 773 | |t Mathematics | ||