Roles of weight functions to a nonlinear porous medium equation with nonlocal source and nonlocal boundary condition

Abstract

In this paper we investigates the blow-up properties of the positive solutions to a porous medium equation with nonlocal reaction source and with nonlocal boundary condition, we obtain the blow-up condition and its blow-up rate estimate.

Blow up problems for a degenerate parabolic equation with nonlocal source and nonlocal nonlinear boundary condition

“…Parabolic equations with both nonlocal sources and nonlocal boundary conditions have been studied as well (see [9][10][11][12]). Lin and Liu [13] considered the problem of the form…”

A Parabolic System With Nonlocal Boundary Conditions and Nonlocal Sources

“…Local existence, global existence and nonexistence of classical solutions were established and blow-up properties were discussed in their work, respectively. Recently, Cui and Yang [6] studied the following porous medium problem with nonlocal boundary condition and nonlocal reaction term…”

Uniform blow-up rate for compressible reactive gas model

“…In recent years, much effort has been devoted to the study of blow-up properties for nonlocal parabolic equations of the above model types [10][11][12][13][14][15][16][17][18][19][20] or their references therein. Deng et al [10] studied the IBVP as…”

“…Employing the ideas in [13] and [14], we describe the blow-up rate of the solution to (1). Unlike some other estimates of the blow-up rate for certain nonlinear parabolic equations (see [15][16][17][18][19][20]), we not only derive the blow-up rate, but also get the accurate coefficient of the blow-up rate. The outline of the present paper is as follows.…”