Existence of global solutions for a system of reaction-diffusion equations with exponential nonlinearity

On Existence and Nonexistence Global Solutions of Reaction-Diffusion Equations

We consider the initial value problem for the reaction-diffusion equation ut = ∆u + f(u). In this paper we show the existence and nonexistence of the global solutions in time. Especially, we extend the condition of the nonlinear terms to more general. We have the results of the existence and the nonexistence for the equation with the nonlinear term f satisfying lim infs→0 f(s)/sp > 0 and lim su...

Existence and Nonexistence of Global Solutions of a Weakly Coupled System of Reaction-Diffusion Equations

Existence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.

Global Existence, Exponential Decay and Blow-Up of Solutions for a Class of Fractional Pseudo-Parabolic Equations with Logarithmic Nonlinearity

In this paper, we study the fractional pseudo-parabolic equations ut +(−4) u+(−4) ut = u log |u|. Firstly, we recall the relationship between the fractional Laplace operator (−4) and the fractional Sobolev space H and discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we derive a threshold result of existence of global w...

A Diffusion Equation with Exponential Nonlinearity Recant Developments

The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...