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Displaying 141 – 160 of 462

Global stability of travelling fronts for a damped wave equation with bistable nonlinearity

Thierry Gallay, Romain Joly (2009)

Annales scientifiques de l'École Normale Supérieure

We consider the damped wave equation $α u_{t t} + u_{t} = u_{x x} - V^{'} (u)$ on the whole real line, where $V$ is a bistable potential. This equation has travelling front solutions of the form $u (x, t) = h (x - s t)$ which describe a moving interface between two different steady states of the system, one of which being the global minimum of $V$ . We show that, if the initial data are sufficiently close to the profile of a front for large $| x |$ , the solution of the damped wave equation converges uniformly on $ℝ$ to a travelling front as $t \to + \infty$ . The proof of this global stability...

Growth of heterotrophe and autotrophe populations in an isolated terrestrial environment

Piotr Paweł Szopa, Monika Joanna Piotrowska (2011)

Applicationes Mathematicae

We consider the model, proposed by Dawidowicz and Zalasiński, describing the interactions between the heterotrophic and autotrophic organisms coexisting in a terrestrial environment with available oxygen. We modify this model by assuming intraspecific competition between heterotrophic organisms. Moreover, we introduce a diffusion of both types of organisms and oxygen. The basic properties of the extended model are examined and illustrated by numerical simulations.

Improved estimates for the Ginzburg-Landau equation : the elliptic case

Fabrice Bethuel, Giandomenico Orlandi, Didier Smets (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We derive estimates for various quantities which are of interest in the analysis of the Ginzburg-Landau equation, and which we bound in terms of the $G L$ -energy $E_{ε}$ and the parameter $ε$ . These estimates are local in nature, and in particular independent of any boundary condition. Most of them improve and extend earlier results on the subject.

Increasing smoothness of solutions to a hyperbolic system on the plane with delay in the boundary conditions.

Lyul'ko, N.A. (2008)

Sibirskij Matematicheskij Zhurnal

Inégalités de Sogge bilinéaires et équation de Schrödinger non linéaire

Nicolas Burq, Patrick Gérard, Nikolay Tzvetkov (2002/2003)

Séminaire Équations aux dérivées partielles

Inégalités $L^{2}$ et représentations de groupes nilpotents

Jean Nourrigat (1985)

Publications mathématiques et informatique de Rennes

Infinity Laplace equation with non-trivial right-hand side.

Lu, Guozhen, Wang, Peiyong (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Influence of diffusion on interactions between malignant gliomas and immune system

Urszula Foryś (2010)

Applicationes Mathematicae

We analyse the influence of diffusion and space distribution of cells in a simple model of interactions between an activated immune system and malignant gliomas, among which the most aggressive one is GBM Glioblastoma Multiforme. It turns out that diffusion cannot affect stability of spatially homogeneous steady states. This suggests that there are two possible outcomes-the solution is either attracted by the positive steady state or by the semitrivial one. The semitrivial steady state describes...

Influence of Vibrations on Convective Instability of Reaction Fronts in Liquids

K. Allali, F. Bikany, A. Taik, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

Propagation of polymerization fronts with liquid monomer and liquid polymer is considered and the influence of vibrations on critical conditions of convective instability is studied. The model includes the heat equation, the equation for the concentration and the Navier-Stokes equations considered under the Boussinesq approximation. Linear stability analysis of the problem is fulfilled, and the convective instability boundary is found depending on...

Influence of Vibrations on Convective Instability of Reaction Fronts in Porous Media

H. Aatif, K. Allali, K. El Karouni (2010)

Mathematical Modelling of Natural Phenomena

The aim of this paper is to study the effect of vibrations on convective instability of reaction fronts in porous media. The model contains reaction-diffusion equations coupled with the Darcy equation. Linear stability analysis is carried out and the convective instability boundary is found. The results are compared with direct numerical simulations.

Instability in semi-infinite strips of solutions of linear systems.

Ramón Quintanilla de la Torre (1986)

Stochastica

The present paper is devoted to study the behaviour at infinity of some solutions of non autonomous and non homogeneous second order linear systems in semi-infinite strips.

Instability of radial standing waves of Schrödinger equation on the exterior of a ball.

Orlando Lopes (1999)

Revista Matemática Complutense

Instability of standing waves for the generalized Davey-Stewartson system

Masahito Ohta (1995)

Annales de l'I.H.P. Physique théorique

Instability of symmetric stationary states for some nonlinear Schrödinger equations with an external magnetic field

J. M. Gonçalves Ribeiro (1991)

Annales de l'I.H.P. Physique théorique

Instability of the stationary solutions of generalized dissipative Boussinesq equation

Amin Esfahani (2014)

Applications of Mathematics

In this work we study the generalized Boussinesq equation with a dissipation term. We show that, under suitable conditions, a global solution for the initial value problem exists. In addition, we derive sufficient conditions for the blow-up of the solution to the problem. Furthermore, the instability of the stationary solutions of this equation is established.

Instability of traveling waves for a generalized diffusion model in population problems.

Liu, Changchun (2004)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Instability of Turing type for a reaction-diffusion system with unilateral obstacles modeled by variational inequalities

Martin Väth (2014)

Mathematica Bohemica

We consider a reaction-diffusion system of activator-inhibitor type which is subject to Turing's diffusion-driven instability. It is shown that unilateral obstacles of various type for the inhibitor, modeled by variational inequalities, lead to instability of the trivial solution in a parameter domain where it would be stable otherwise. The result is based on a previous joint work with I.-S. Kim, but a refinement of the underlying theoretical tool is developed. Moreover, a different regime of parameters...

Interaction contrôlée dans les équations aux dérivées partielles non linéaires

J.-Y. Chemin (1988)

Bulletin de la Société Mathématique de France

Interpolation spaces and weighted pseudo almost automorphic solutions to parabolic equations and applications to fluid dynamics

Thieu Huy Nguyen, Thi Ngoc Ha Vu, The Sac Le, Truong Xuan Pham (2022)

Czechoslovak Mathematical Journal

We investigate the existence, uniqueness and polynomial stability of the weighted pseudo almost automorphic solutions to a class of linear and semilinear parabolic evolution equations. The necessary tools here are interpolation spaces and interpolation theorems which help to prove the boundedness of solution operators in appropriate spaces for linear equations. Then for the semilinear equations the fixed point arguments are used to obtain the existence and stability of the weighted pseudo almost...

Invariance of the Gibbs measure for the Benjamin–Ono equation

Yu Deng (2015)

Journal of the European Mathematical Society

In this paper we consider the periodic Benjemin-Ono equation.We establish the invariance of the Gibbs measure associated to this equation, thus answering a question raised in Tzvetkov [28]. As an intermediate step, we also obtain a local well-posedness result in Besov-type spaces rougher than $L^{2}$ , extending the $L^{2}$ well-posedness result of Molinet [20].

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