Estimates for the blowup time of a combustion model with nonlocal heat sources

Abstract

Please cite this article in press as: N. Wang et al., Estimates for the blowup time of a combustion model with nonlocal heat sources, J. Math. Anal. Appl. (2016), http://dx. AbstractIn this paper, we establish the lower and upper bounds for the blowup time of the solution to a system of parabolic equations with nonlocal nonlinearities which appears in a model of combustion. Different techniques are applied to deal with the problems in different space dimensions. We also discuss non-simultaneous blowup phenomenon of the solution.

Time‐weighted blow‐up rates and pointwise profile for single‐point blow‐up solutions in reaction–diffusion equations

“…It can be found that the blow-up time T is nonincreasing in the size of the initial data (e.g., [13,14]). Then we can choose suitable initial data such that 1 ˇT C˛T > 0 due toˇ>˛.…”

“…The results about Fujita blow-up phenomena in unbounded domains can be found in [7,8] and the references cited there. For fully coupled systems, one can refer to [9][10][11][12][13][14][15][16][17][18][19][20][21] for singularity of solutions. For singular or degenerate problems, one can find the corresponding results in [22][23][24].…”

Lower Bounds of Blow Up Time for a Class of Slow Reaction Diffusion Equations with Inner Absorption Terms

“…Inspired by Refs. [8][9][10][11][12][13][14][15][16], this paper studies the lower bound of blow up time for solutions of slow reaction-diffusion equations (1)-( 5) with different boundary conditions when m > 1n > 1, and generalizes the existing results. The results can better describe the reaction diffusion problems with the cross influence of two variables in physical, chemical and hydrodynamic problems.…”

Lower Bound Estimate of Blow Up Time for the Porous Medium Equations under Dirichlet and Neumann Boundary Conditions

“…Blow-up at a finite time and lower bound of blowing up time of solution for the parabolic equations are studied in [4,5]. The lower bound of blowing up time for solutions of other similar equations or equation set is shown in [6][7][8][9].…”