Related papers: Optimal extinction rates for the fast diffusion eq…
The change in the decay rate of an excited atom that is brought about by extinction and thermal-radiation effects in a nearby dielectric medium is determined from a quantummechanical model. The medium is a collection of randomly distributed…
Consider a supercritical branching random walk in a time-inhomogeneous random environment. We impose a selection (called barrier) on survival in the following way. The position of the barrier may depend on the generation and the…
In this paper we propose a numerical method to approximate the best decay rate for some dissipative systems that are bounded perturbation of unbounded skew-adjoint operators. We also give some numerical examples and applications to…
We study the high frequency limit for a non-dissipative Helmholtz equation. We first prove the absence of eigenvalue on the upper half-plane and close to an energy which satisfies a weak damping assumption on trapped trajectories. Then we…
We consider stochastic non-linear diffusion equations with a highly singular diffusivity term and multiplicative gradient-type noise. We study existence and uniqueness of non-negative variational solutions in terms of stochastic variational…
We study the large time behavior of non-negative solutions to the singular diffusion equation with gradient absorption $$ \partial_t u-\Delta_{p}u+|\nabla u|^q=0 \quad \hbox{in} \ (0,\infty)\times\real^N, $$ for $p_c:=2N/(N+1)
The effect of diffusively correlated spatial fluctuations on the proliferation-extinction transition of autocatalytic agents is investigated numerically. Reactants adaptation to spatio-temporal active regions is shown to lead to…
In this paper we are concerned with the convergence rate of solutions to the three-dimensional turbulent flow equations. By combining the $L^p$-$L^q$ estimates for the linearized equations and an elaborate energy method, the convergence…
This paper completes some previous studies by several authors on the finite time extinction for nonlinear Schr{\"o}dinger equation when the nonlinear damping term corresponds to the limit cases of some ``saturating non-Kerr law''…
This paper is devoted to the study of the persistence versus extinction of species in the reaction-diffusion equation: \begin{equation} u_t-\Delta u=f(t,x_1-ct,y,u) \quad\quad t>0,\ x\in\Omega,\nonumber \end{equation} where $\Omega$ is of…
We obtain new estimates for the solution of both the porous medium and the fast diffusion equations by studying the evolution of suitable Lipschitz norms. Our results include instantaneous regularization for all positive times, long-time…
In this work, exact solutions are derived for an integer- and fractional-order time-delayed diffusion equation with arbitrary initial conditions. The solutions are obtained using Fourier transform methods in conjunction with the known…
A sample of 59 sight lines to reddened Galactic OB stars was examined for correlations of the strength of the CO Fourth Positive (A - X) absorption band system with the ultraviolet interstellar extinction curve parameters. We used archival…
We analyze the spectral properties and peculiar behavior of solutions of a damped wave equation on a finite interval with a singular damping of the form $\alpha/x$, $\alpha>0$. We establish the exponential stability of the semigroup for all…
We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the…
We consider a damped wave equation in a bounded domain. The damping is nonlinear and is homogeneous with degree p -- 1 with p > 2. First, we show that the energy of the strong solution in the supercritical case decays as a negative power of…
A wide range of stochastic processes that model the growth and decline of populations exhibit a curious dichotomy: with certainty either the population goes extinct or its size tends to infinity. There is a elegant and classical theorem…
This paper provides a full characterization of the value function and solution(s) of an optimal stopping problem for a one-dimensional diffusion with an integral criterion. The results hold under very weak assumptions, namely, the diffusion…
Blow-up rates are established for general solutions to the quasilinear diffusion equation $$ \partial_tu=\Delta u^m+|x|^{\sigma}u^p, \quad (x,t)\in\mathbb{R}^N\times(0,T), $$ in the range of exponents $1<p<m$, $\sigma>0$. More precisely, if…
Let $\Omega\subset\R^n$ be a smooth bounded domain and let $a_1,a_2,\dots,a_{i_0}\in\Omega$, $\widehat{\Omega}=\Omega\setminus\{a_1,a_2,\dots,a_{i_0}\}$ and $\widehat{R^n}=\R^n\setminus\{a_1,a_2,\dots,a_{i_0}\}$. We prove the existence of…