Zhong Bo Fang

On the (p, h)-convex function and some integral inequalities

In this paper, we introduce a new class of (p,h)-convex functions which generalize P-functions and convex, h,p,s-convex, Godunova-Levin functions, and we give some properties of the functions. Moreover, we establish the corresponding Schur, Jensen, and Hadamard types of inequalities.MSC:35K65, 35B33, 35B40.

Global existence and blow-up of solutions for p-Laplacian evolution equation with nonlinear memory term and nonlocal boundary condition

In this paper, we deal with an initial boundary value problem for a p-Laplacian evolution equation with nonlinear memory term and inner absorption term subject to a weighted linear nonlocal boundary condition. We find the effects of a weighted function as regards determining blow-up of nonnegative solutions or not and establish the precise blow-up estimate for the linear diffusion case under some suitable conditions.

Extinction and decay estimates of solutions for a porous medium equation with nonlocal source and strong absorption

In this paper, we investigate extinction properties of the solutions for the initial Dirichlet boundary value problem of a porous medium equation with nonlocal source and strong absorption terms. We obtain some sufficient conditions for the extinction of nonnegative nontrivial weak solutions and the corresponding decay estimates which depend on the initial data, coefficients, and domains.

Extinction and decay estimates of solutions for a p-Laplacian evolution equation with nonlinear gradient source and absorption

We investigate the extinction properties of non-negative nontrivial weak solutions of the initial-boundary value problem for a p-Laplacian evolution equation with nonlinear gradient source and absorption terms.MSC:35K65, 35B33, 35B40.

Existence and nonexistence of entire positive solutions for (p,q)-Laplacian elliptic system with a gradient term

This work is concerned with the entire positive solutions for a (p,q)-Laplacian elliptic system of equations with a gradient term. We find the sufficient condition for nonexistence of entire large positive solutions and existence of infinitely many entire solutions, which are large or bounded.

A note on blow-up of solutions for the nonlocal quasilinear parabolic equation with positive initial energy

In this short note, we consider a nonlocal quasilinear parabolic equation in a bounded domain with the Neumann-Robin boundary condition. We establish a blow-up result for a certain solution with positive initial energy.

Lower bounds for blow-up time in nonlocal parabolic problem under Robin boundary conditions

ABSTRACT This paper deals with the blow-up phenomenon for a nonlocal reaction diffusion equation with time-dependent coefficient in a bounded star-shaped domain under Robin boundary condition. Using the auxiliary function method and differential inequality technique, lower bounds for the blow-up time can be obtained if the blow-up occurs in finite time. Some examples are presented to illustrate applications of our results.

Roles of Weight Functions to a Nonlocal Porous Medium Equation with Inner Absorption and Nonlocal Boundary Condition

This work is concerned with an initial boundary value problem for a nonlocal porous medium equation with inner absorption and weighted nonlocal boundary condition. We obtain the roles of weight function on whether determining the blowup of nonnegative solutions or not and establish the precise blow-up rate estimates under some suitable condition.

Blow-up analysis for a nonlocal reaction-diffusion system with time-dependent coefficients

ABSTRACT A blow-up analysis for a nonlocal reaction-diffusion system with time-dependent coefficients is investigated under null Dirichlet boundary conditions. Based on the Kaplans method, comparison principle and modified differential inequality technique, we establish a blow-up criteria and derive the bounds for the blow-up time under the appropriate measures in whole-dimensional space.

Blow-up phenomena for a quasilinear parabolic equation with inner source and nonlinear boundary condition

Abstract In this paper, we deal with blow-up phenomena to a quasilinear parabolic equation with inner source and nonlinear boundary condition. By the technique of differential inequality, we establish a lower bound for the blow-up time if blow-up does occur. Furthermore, we consider a specific class of problems to guarantee occurrence of blow-up and derive an upper bound for the blow-up time.