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Quantitative Estimates of the Threshold Phenomena for Propagation in Reaction-Diffusion Equations [PDF]

SIAM Journal on Applied Dynamical Systems, 2019
We focus on the (sharp) threshold phenomena arising in some reaction-diffusion equations supplemented with some compactly supported initial data. In the so-called ignition and bistable cases, we prove the first sharp quantitative estimate on the (sharp ...
M. Alfaro, A. Ducrot, Grégory Faye
semanticscholar   +1 more source

Asymptotic analysis for a weakly damped wave equation with application to a problem arising in elasticity

Journal of Function Spaces, Volume 8, Issue 1, Page 17-54, 2010., 2010
The present work is devoted to the study of homogenization of the weakly damped wave equation ∫Ωρε∂2uε∂t2(t)⋅υdx+2ε2μ∫ΩfεEij(∂uε∂t(t))Eij(υ)dx+ε2λ∫Ωfεdiv(∂uε∂t(t))div υdx+ϑ∫Ωfεdiv(uε(t))divυdx=∫Ωf(t) · υdx for all υ=(υ1, υ2, υ3) ∈ Vε(0 < t < T), with initial conditions uε(0)=∂uε∂t(0)=ω (the origin in ℝ3). Convergence homogenization results are achieved
Gabriel Nguetseng, Hubert Nnang, Nils Svanstedt, Lars-Erik Persson   +3 more
wiley   +1 more source

Stability of combination of rarefaction waves with viscous contact wave for compressible Navier-Stokes equations with temperature-dependent transport coefficients and large data

Advances in Nonlinear Analysis, 2022
In this article, we study the large-time behavior of combination of the rarefaction waves with viscous contact wave for a one-dimensional compressible Navier-Stokes system whose transport coefficients depend on the temperature.
Dong Wenchao, Guo Zhenhua
doaj   +1 more source

Reiterated homogenization of nonlinear monotone operators in a general deterministic setting

Journal of Function Spaces, Volume 7, Issue 2, Page 121-152, 2009., 2009
We study reiterated homogenization of a nonlinear non‐periodic elliptic differential operator in a general deterministic setting as opposed to the usual stochastic setting. Our approach proceeds from an appropriate notion of convergence termed reiterated Σ‐convergence.
Dag Lukkassen, Gabriel Nguetseng, Hubert Nnang, Peter Wall, Björn Birnir   +4 more
wiley   +1 more source

Two‐scale convergence with respect to measures and homogenization of monotone operators

Journal of Function Spaces, Volume 3, Issue 2, Page 125-161, 2005., 2005
In 1989 Nguetseng introduced two‐scale convergence, which now is a frequently used tool in homogenization of partial differential operators. In this paper we discuss the notion of two‐scale convergence with respect to measures. We make an exposition of the basic facts of this theory and develope it in various ways.
Dag Lukkassen, Peter Wall, Lars-Erik Persson   +2 more
wiley   +1 more source

Existence of random attractors and the upper semicontinuity for small random perturbations of 2D Navier-Stokes equations with linear damping

Open Mathematics, 2021
The incompressible 2D stochastic Navier-Stokes equations with linear damping are considered in this paper. Based on some new calculation estimates, we obtain the existence of random attractor and the upper semicontinuity of the random attractors as ε→0 ...
Li Haiyan, Wang Bo
doaj   +1 more source

A note on resonant frequencies for a system of elastic wave equations

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 64, Page 3485-3498, 2004., 2004
We present a rather simple proof of the existence of resonant frequencies for the direct scattering problem associated to a system of elastic wave equations with Dirichlet boundary condition. Our approach follows techniques similar to those in Cortés‐Vega (2003).
Luis A. Cortés-Vega
wiley   +1 more source

On a fractional Schrödinger-Poisson system with strong singularity

Open Mathematics, 2021
We investigate a fractional Schrödinger-Poisson system with strong singularity as follows: (−Δ)su+V(x)u+λϕu=f(x)u−γ,x∈R3,(−Δ)tϕ=u2,x∈R3,u>0,x∈R3,\left\{\begin{array}{ll}{\left(-\Delta )}^{s}u+V\left(x)u+\lambda \phi u=f\left(x){u}^{-\gamma },& x\in ...
Yu Shengbin, Chen Jianqing
doaj   +1 more source

Properties of entire solutions of some linear PDE's

, 2017
In this paper, there are improved sufficient conditions of boundedness of the L-index in a direction for entire solutions of some linear partial differential equations. They are new even for the one-dimensional case and 1.
Andriy Ivanovych Bandura, O. Skaskiv, P. Filevych   +2 more
semanticscholar   +1 more source

Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 14, Page 721-739, 2004., 2004
We study a family of diffusion models for compounded risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. We are interested in the models in which the dividend payments are paid from the risk reserves.
S. Shao, C. L. Chang
wiley   +1 more source