Nonexistence of global solutions for an inhomogeneous pseudo-parabolic equation

Existence and Nonexistence of Global Solutions of a Fully Nonlinear Parabolic Equation

In the paper, we study the global existence of weak solution of the fully nonlinear parabolic problem (1.1)-(1.3) with nonlinear boundary conditions for the situation without strong absorption terms. Also, we consider the blow up of global solution of the problem (1.1)-(1.3) by using the convexity method.

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Existence and Nonexistence of Global Solutions in Time for a Reaction-Diffusion System with Inhomogeneous Terms

We consider the initial value problem for the reaction-diffusion system with inhomogeneous terms. In this paper we show the existence and nonexistence of global solution in time. Especially, for the nonexistence we extend the conditions of the nonlinear terms and the initial data to the weaker conditions. We prove that for the nonlinear term and the initial data whose support is included in som...

Nonexistence of Global Solutions in Time for Reaction-Diffusion Systems with Inhomogeneous Terms in Cones

We consider initial-boundary value problems for the reaction-diffusion systems with inhomogeneous terms in cones. In this paper we show the nonexistence of global solutions of the problems in time. Keyword and Phrases: reaction-diffusion, global nonexistence, inhomogeneous term, cone. AMS subject classifications: 35K45, 35K57.

Existence and nonexistence of positive solutions of semilinear elliptic equation with inhomogeneous strong Allee effect

In this paper, we study a semilinear elliptic equation defined on a bounded smooth domain. This type of problem arises from the study of spatial ecology model, and the growth function in the equation has a strong Allee effect and is inhomogeneous. We use variational methods to prove that the equation has at least two positive solutions for a large parameter if it satisfies some appropriate cond...