Global existence of solutions of semilinear heat equation with nonlinear memory condition

We consider a semilinear parabolic equation with flux at the boundary governed by a nonlinear memory. We give some conditions for this problem which guarantee global existence of solutions as well as blow up in finite time of all nontrivial solutions. The results depend on the behavior of variable coefficients as $t \to \infty.

A Note on nonexistence of radial solutions to semilinear elliptic inequations

We study the nonexistence result of radial solutions to -[Delta]u + [formula] posed in B or in B \ {0} where B is the unit ball centered at the origin in RN, N [greater than or equal] 3. Moreover, we give a complete classification of radial solutions to the problem [formula]. In particular we prove that the latter has exactly one family of radial solutions

Influence of variable coefficients on global existence of solutions of semilinear heat equations with nonlinear boundary conditions

We consider semilinear parabolic equations with nonlinear boundary conditions. We give conditions which guarantee global existence of solutions as well as blow-up in finite time of all solutions with nontrivial initial data. The results depend on the behavior of variable coefficients as $t \to \infty$

The Cauchy problem for ut=Δu+|∇u|q

AbstractWith q a positive real number, the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces. In that context it is known as the generalized deterministic KPZ equation. The paper is concerned with the initial-value problem for the equation under the assumption that the initial-data function is bounded and continuous. Results on the existence, uniqueness, and regularity of solutions are obtained

Uniform boundedness and extinction results of solutions to a predator–prey system

Global existence, positivity, uniform boundedness and extinction results of solutions to a system of reaction-diffusion equations on unbounded domain modeling two species on a predator–prey relationship is considered