Interactions of Elementary Waves for the Nonlinear Chromatography Equations∗
نویسندگان
چکیده
Abstract. In this article, we study the global solution of the elementary waves interaction problem for the nonlinear chromatography equations. We constructively obtain the solutions when the initial data are three piecewise constant states. The global structures and large time-asymptotic behaviors of the solutions are analyzed case by case. During the process of the interaction, it is easy to see that the solutions of the perturbed Riemann problem converge to nothing but the corresponding Riemann solutions as → 0, from which the stability of the Riemann solutions with respect to this local small perturbation of the Riemann initial data are obtained.
منابع مشابه
A Study of Bit Condition for Generation Rx -Mode Waves: Interaction of Particles with Z/UH-Mode Waves
Interactions of charge particles with electromagnetic waves have important effects (linear and nonlinear) on the propagation of electromagnetic waves, and it can somewhat play a role in generation of the new mode waves. Besides, the particle energies can play an important role in causing instability in plasma. The values of parallel energy of the particles have been calculated so that they can ...
متن کاملAnalytical Investigation of TM Surface Waves in 1D Photonic Crystals Capped by a Self-Focusing Left-Handed Slab
In this paper, the localized TM surface waves of a nonlinear self-focusingleft-handed slab sandwiched between a uniform medium and a one-dimensionalphotonic crystal (1D PC) is analytically investigated. Our method is based on the firstintegral of the nonlinear Maxwell's equations. For the TM surface waves, the presenceof two electric field components makes the analysis difficult. Therefore, we ...
متن کاملSome traveling wave solutions of soliton family
Solitons are ubiquitous and exist in almost every area from sky to bottom. For solitons to appear, the relevant equation of motion must be nonlinear. In the present study, we deal with the Korteweg-deVries (KdV), Modied Korteweg-de Vries (mKdV) and Regularised LongWave (RLW) equations using Homotopy Perturbation method (HPM). The algorithm makes use of the HPM to determine the initial expansion...
متن کاملA numerical investigation of a reaction-diffusion equation arises from an ecological phenomenon
This paper deals with the numerical solution of a class of reaction diffusion equations arises from ecological phenomena. When two species are introduced into unoccupied habitat, they can spread across the environment as two travelling waves with the wave of the faster reproducer moving ahead of the slower.The mathematical modelling of invasions of species in more complex settings that include ...
متن کاملFundamental Solution and Study of Plane Waves in Bio-Thermoelastic Medium with DPL
The fundamental solution of the system of differential equations in bio-thermoelasticity with dual phase lag (DPL) in case of steady oscillations in terms of elementary function is constructed and basic property is established. The tissue is considered as an isotropic medium and the propagation of plane harmonic waves is studied. The Christoffel equations are obtained and modified with the ther...
متن کامل