Asymptotic behavior for a class of the renewal nonlinear equation with diffusion

We prove that there exists a unique very singular solution of the equation, which has self-similar form and we show the convergence of general solutions with suitable initial

However, the local well-posedness proved in [16, 7] provides more information on the solutions, for instance, one knows that the global solutions to the defocusing (INLS) satisfy u ∈

Convergence of a finite element method for the drift-diffusion semiconductor device equations: the zero diffusion case... Thermal equilibrium at the boundary in 2-D: evolution of

We now prove the existence of a stationary solution to (1.1) when the overall fragmentation rate a may be bounded for large sizes but does not decay to zero.. As in Lemma 7.1, the

In contrast to the small size behavior which is dominated by the properties of the daughter distribution function b, the behavior of f for large sizes is determined by the

We show that the entropy method can be used to prove exponential con- vergence towards equilibrium with explicit constants when one considers a reaction-diffusion system

1. Fibich [7] noted that in the nonlinear optics context, the origin of the nonlinear damping is multiphoton absorption. Damped Nonlinear Schr¨ odinger Equation, Blow-up,

Abstract : We prove here global existence in time of weak solutions for some reaction- diffusion systems with natural structure conditions on the nonlinear reactive terms which