Related papers: Speed selection for coupled wave equations
In this paper we consider a singular wave equation with distributional and more singular non-distributional coefficients and develop tools and techniques for the phase-space analysis of such problems. In particular we provide a detailed…
We investigate the long time behaviour of the $L^2$-energy of solutions to wave equations with variable speed. The novelty of the approach is the combination of estimates for higher order derivatives of the coefficient with a stabilisation…
We consider reaction-diffusion equations of porous medium type, with different kind of reaction terms, and nonnegative bounded initial data. For all the reaction terms under consideration there are initial data for which the solution…
Stability of a set of travelling wave solutions to the hyperbolic generalization of the convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.
wave solutions to nonlinear partial differential equations. We simplify the so called (G'/G)-expansion method and apply two of those methods to simple physical problems.
Models for the dynamics of congestion control generally involve systems of coupled differential equations. Universally, these models assume that traffic sources saturate the maximum transmissions allowed by the congestion control method.…
We examine travelling wave solutions of the reaction-diffusion equation, $\partial_t u= R(u) + \partial_x \left[D(u) \partial_x u\right]$, with a Stefan-like condition at the edge of the moving front. With only a few assumptions on $R(u)$…
In this paper, we study the numerical stabilization of a 1D system of two wave equations coupled by velocities with an internal, local control acting on only one equation. In the theoretical part of this study, we distinguished two cases.…
For any kind of wave phenomenon one can find ways to derive the respective dispersion relation from experimental observations and measurements. This dispersion relation determines the structure of the wave equation and thus characterizes…
We present a method to control the position as a function of time of one-dimensional traveling wave solutions to reaction-diffusion systems according to a pre-specified protocol of motion. Given this protocol, the control function is found…
We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and…
Choosing ${\kappa}$ (horizontal ordinate of the saddle point associated to the homoclinic orbit) as bifurcation parameter, bifurcations of the travelling wave solutions is studied in a perturbed $(1 + 1)$-dimensional dispersive long wave…
For certain values of the wave speed parameter, evolution equations for the temperature of a region of fuel admit traveling wave solutions describing fire fronts. We consider such a system in the form of a nonlinear reaction-diffusion…
Numerical modelling of coupled multiphysics phenomena is becoming an increasingly important subject in applied mathematics. The main challenge in teaching this subject is the complexity of both the mathematical models and their numerical…
We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of…
Obtaining the total wavefunction evolution of interacting quantum systems provides access to important properties, such as entanglement, shedding light on fundamental aspects, e.g. quantum energetics and thermodynamics, and guiding towards…
A kinetic flux-splitting procedure used in conjunction with local thermodynamic equilibrium in a finite volume allows us to investigate numerically discrete-velocity gas flows. The procedure, outlined for a general discrete-velocity gas, is…
We consider a heavy, uniform, elastic beam rested on periodically distributed supports as a simplified model of a bridge. The supports are subjected to a partial destruction propagating as a failure wave along the beam. Three related models…
Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…