Asymptotic analysis for reaction-diffusion equations with absorption

Asymptotic States for Equations of Reaction and Diffusion

Reaction-Diffusion equations with applications

Well-posedness and asymptotic behavior for stochastic reaction-diffusion equations with multiplicative Poisson noise∗

We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations with a polynomially growing quasi-monotone nonlinearity and multiplicative Poisson noise. We also study existence and uniqueness of invariant measures for the associated semigroup in the Markovian case. A key role is played by a new maximal inequality for stochastic convolutions in Lp spaces .

Asymptotic behavior for a singular diffusion equation with gradient absorption

We study the large time behavior of non-negative solutions to the singular diffusion equation with gradient absorption ∂ t u − ∆ p u + |∇u| q = 0 in (0, ∞) × R N , for p c := 2N/(N + 1) < p < 2 and p/2 < q < q * := p − N/(N + 1). 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 ...

Asymptotic Behavior for Nonlocal Diffusion Equations

We study the asymptotic behavior for nonlocal diffusion models of the form ut = J ∗ u − u in the whole R or in a bounded smooth domain with Dirichlet or Neumann boundary conditions. In R we obtain that the long time behavior of the solutions is determined by the behavior of the Fourier transform of J near the origin, which is linked to the behavior of J at infinity. If Ĵ(ξ) = 1 − A|ξ| + o(|ξ|) ...