Periodic solution of a quasilinear parabolic equation with nonlocal terms and Neumann boundary conditions

A Quasilinear Parabolic System with Nonlocal Sources and Weighted Nonlocal Boundary Conditions

Abstract In this paper, we investigate the blow-up properties of a quasilinear reaction-diffusion system with nonlocal nonlinear sources and weighted nonlocal Dirichlet boundary conditions. The critical exponent is determined under various situations of the weight functions. It is observed that the boundary weight functions play an important role in determining the blow-up conditions. In additi...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Numerical Solution for Parabolic Equation with Nonlocal Conditions

In this paper, we study a parabolic equation with purely nonlocal (integral) conditions. We present a numerical approximate solution by Laplace transform method. Some experimental numerical results using the proposed numerical procedure are discussed.

A Quasilinear Parabolic System with Nonlocal Boundary Condition

We investigate the blow-up properties of the positive solutions to a quasilinear parabolic system with nonlocal boundary condition. We first give the criteria for finite time blowup or global existence, which shows the important influence of nonlocal boundary. And then we establish the precise blow-up rate estimate. These extend the resent results of Wang et al. 2009 , which considered the spec...

Nonlocal Problems with Neumann Boundary Conditions

We introduce a new Neumann problem for the fractional Laplacian arising from a simple probabilistic consideration, and we discuss the basic properties of this model. We can consider both elliptic and parabolic equations in any domain. In addition, we formulate problems with nonhomogeneous Neumann conditions, and also with mixed Dirichlet and Neumann conditions, all of them having a clear probab...