Lower Bounds Estimate for the Blow-Up Time of a Slow Diffusion Equation with Nonlocal Source and Inner Absorption

2018

Bound Value Probl

Self Cite

We investigate the blow-up phenomena for a porous medium equation with weighted nonlocal source and inner absorption terms subject to null Dirichlet boundary condition. Based on a modified differential inequality technique, we establish some sufficient conditions to guarantee the existence of non-global solutions to the model and also derive the upper bounds for the blow-up time. Moreover, the lower bounds for the blow-up time are obtained under some appropriate measure in the whole-dimensional space (N ≥ 1).

Section: Resultssupporting

confidence: 57%

“…They obtained the lower bounds for blow-up time of the blow-up solution to the initial boundary value problem in a three-dimensional space. Specially, Fang et al [20] studied…”

Section: Introductionmentioning

confidence: 99%

Bounds for the blow-up time of a porous medium equation with weighted nonlocal source and inner absorption terms

Shen

2018

Bound Value Probl

Self Cite

“…They obtain a lower bound for the blow‐up time of the solution in a convex bounded domain

normalΩ \subset {double-struckR}^{N} (N \geq 3)

. To see some studies on quasilinear parabolic equations, non‐local reaction diffusion problem, and a semilinear parabolic equation with time‐dependent coefficients, refer to .…”

Section: Introductionmentioning

confidence: 99%

Blow‐up phenomena for a semilinear parabolic equation with weighted inner absorption under nonlinear boundary flux

Math Methods in App Sciences

2016

Self Cite

Communicated by S. A. MessaoudiBlow-up phenomena for a nonlinear divergence form parabolic equation with weighted inner absorption term are investigated under nonlinear boundary flux in a bounded star-shaped region. We assume some conditions on weight function and nonlinearities to guarantee that the solution exists globally or blows up at finite time. Moreover, by virtue of the modified differential inequality, upper and lower bounds for the blow-up time of the solution are derived in higher dimensional spaces. Three examples are presented to illustrate applications of our results.

“…Under somewhat more restrictive conditions, a lower bound for t * was also derived. To see some studies on quasilinear parabolic equations, refer to [12,13].…”

Section: Introductionmentioning

confidence: 99%

Blow-up analysis for a semilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux

Wang

2015

Z. Angew. Math. Phys.

Self Cite

A blow-up analysis for a nonlinear divergence form of parabolic equation with time-dependent coefficients is given under nonlinear boundary flux in a bounded star-shaped region. We establish some conditions on time-dependent coefficients and nonlinearities to guarantee existence of global solution or blow-up solution at some finite time t * . Moreover, an upper bound for t * is derived. Under somewhat more restrictive conditions, a lower bound for t * can be obtained. Finally, some application examples to verify the bounds of t * are presented.Mathematics Subject Classification. 35K65 · 35B30 · 35B40.