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Global Existence and Blow-Up of Solutions to a Parabolic Nonlocal Equation Arising in a Theory of Thermal Explosion
- Source :
- Journal of Function Spaces, Vol 2022 (2022)
- Publication Year :
- 2022
- Publisher :
- Wiley, 2022.
-
Abstract
- 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.
- Subjects :
- Mathematics
QA1-939
Subjects
Details
- Language :
- English
- ISSN :
- 23148888
- Volume :
- 2022
- Database :
- Directory of Open Access Journals
- Journal :
- Journal of Function Spaces
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.75b0e6b3e948539146a69215318982
- Document Type :
- article
- Full Text :
- https://doi.org/10.1155/2022/4629799