Back to Search
Start Over
A complete characterization of the discrete p-Laplacian parabolic equations with q-nonlocal reaction with respect to the blow-up property.
- Source :
-
Journal of Mathematical Analysis & Applications . May2019, Vol. 473 Issue 2, p1447-1473. 27p. - Publication Year :
- 2019
-
Abstract
- Abstract In this paper, we consider the following discrete p -Laplacian nonlinear parabolic equations with q -nonlocal reaction { u t (x , t) = Δ p , ω u (x , t) + λ ∑ y ∈ S | u (y , t) | q − 1 u (y , t) , (x , t) ∈ S × (0 , ∞) , u (x , t) = 0 , (x , t) ∈ ∂ S × (0 , ∞) , u (x , 0) = u 0 ≥ 0 , x ∈ S ‾. Here, S is a network with boundary ∂ S. The goal of this paper is to characterize completely the parameters p > 1 and q > 0 to see when the solution blows up, vanishes, or exists globally. Indeed, the blow-up rates for the blow-up solutions are derived. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 473
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 134404126
- Full Text :
- https://doi.org/10.1016/j.jmaa.2019.01.031