Results 51 to 60 of about 93 (92)

A singular perturbation result for a class of periodic-parabolic BVPs

Open Mathematics
In this article, we obtain a very sharp version of some singular perturbation results going back to Dancer and Hess [Behaviour of a semilinear periodic-parabolic problem when a parameter is small, Lecture Notes in Mathematics, Vol. 1450, Springer-Verlag,
Cano-Casanova Santiago, Fernández-Rincón Sergio, López-Gómez Julián   +2 more
doaj   +1 more source

Singular Perturbation for Controlled Wave Equations

, 1994
In this paper we study the approximation of the solutions to an optimal control problem with distributed parameters for the wave equation, let's say P, through solutions of a sequence of regularized problems P ffl .
Francesca Bucci
core  

Existence and uniqueness of solution for a singular elliptic differential equation

Advances in Nonlinear Analysis
In this article, we are concerned about the existence, uniqueness, and nonexistence of the positive solution for: −Δu−12(x⋅∇u)=μh(x)uq−1+λu−up,x∈RN,u(x)→0,as∣x∣→+∞,\left\{\begin{array}{l}-\Delta u-\frac{1}{2}\left(x\cdot \nabla u)=\mu h\left(x){u}^{q-1}+\
Gu Shanshan, Yang Bianxia, Shao Wenrui
doaj   +1 more source

On a Cahn–Hilliard equation for the growth and division of chemically active droplets modelling protocells

European Journal of Applied Mathematics
The Cahn–Hilliard model with reaction terms can lead to situations in which no coarsening is taking place and, in contrast, growth and division of droplets occur which all do not grow larger than a certain size.
Harald Garcke, Kei Fong Lam, Robert Nürnberg, Andrea Signori   +3 more
doaj   +1 more source

Boundary Layers in a Semilinear Parabolic Problem

, 2007
We study a singular perturbation problem for a certain type of reaction diffusion equation with a space-dependent reaction term. We compare the effect that the presence of boundary layers versus internal layers has on the existence and stability of ...
Domingo Salazar, Jack K. Hale
core  

The evolution problem for the 1D nonlocal Fisher-KPP equation with a top hat kernel. Part 2. The initial-boundary value problem on a finite domain

European Journal of Applied Mathematics
In the second part of this series of papers, we address the same evolution problem that was considered in part 1 (see [16]), namely the nonlocal Fisher-KPP equation in one spatial dimension, \begin{equation*} u_t = D u_{xx} + u(1-\phi *u), \end ...
David J. Needham, John Billingham
doaj   +1 more source

The evolution problem for the 1D nonlocal Fisher-KPP equation with a top hat kernel. Part 1. The Cauchy problem on the real line

European Journal of Applied Mathematics
We study the Cauchy problem on the real line for the nonlocal Fisher-KPP equation in one spatial dimension, \begin{equation*} u_t = D u_{xx} + u(1-\phi *u), \end{equation*} where $\phi *u$ is a spatial convolution with the top hat kernel,
David John Needham, John Billingham, Nikolaos Michael Ladas, John Meyer   +3 more
doaj   +1 more source

Modelling microtube driven invasion of glioma. [PDF]

J Math Biol, 2023
Hillen T, Loy N, Painter KJ, Thiessen R.
europepmc   +1 more source

A geometric approach to pinned pulses in a class of non-autonomous reaction–diffusion equations

European Journal of Applied Mathematics
This paper develops a geometric and analytical framework for studying the existence and stability of pinned pulse solutions in a class of non-autonomous reaction–diffusion equations.
Yuanxian Chen, Jianhe Shen
doaj   +1 more source

Non local evolution equations and phase transition problems

, 2013
L'objet de cette thèse est d'étudier le comportement en temps long de solutions d'équations d'évolution non locales ainsi que la limite singulière d'équations et de systèmes d'équations aux dérivées partielles, où intervient un petit paramètre epsilon ...
Nguyen, Thanh Nam
core