The Local Strong and Weak Solutions for a Nonlinear Dissipative Camassa-Holm Equation
نویسندگان
چکیده
and Applied Analysis 3 2. Main Results Firstly, we give some notation. The space of all infinitely differentiable functions φ t, x with compact support in 0, ∞ ×R is denoted byC∞ 0 . L L R 1 ≤ p < ∞ is the space of all measurable functions h such that ‖h‖pLp ∫ R |h t, x |pdx < ∞. We define L∞ L∞ R with the standard norm ‖h‖L∞ infm e 0supx∈R\e|h t, x |. For any real number s, H H R denotes the Sobolev space with the norm defined by
منابع مشابه
H−perturbations of Smooth Solutions for a Weakly Dissipative Hyperelastic-rod Wave Equation
We consider a weakly dissipative hyperelastic-rod wave equation (or weakly dissipative Camassa–Holm equation) describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. By fixed a smooth solution, we establish the existence of a strongly continuous semigroup of global weak solutions for any initial perturbation from H1(R). In particular, the supersonic solitary shock w...
متن کاملOn Time Fractional Modifed Camassa-Holm and Degasperis-Procesi Equations by Using the Haar Wavelet Iteration Method
The Haar wavelet collocation with iteration technique is applied for solving a class of time-fractional physical equations. The approximate solutions obtained by two dimensional Haar wavelet with iteration technique are compared with those obtained by analytical methods such as Adomian decomposition method (ADM) and variational iteration method (VIM). The results show that the present scheme is...
متن کاملA Singular Limit Problem for Conservation Laws Related to the Camassa-holm Shallow Water Equation
We consider a shallow water equation of Camassa-Holm type, containing nonlinear dispersive effects as well as fourth order dissipative effects. We prove that as the diffusion and dispersion parameters tend to zero, with a condition on the relative balance between these two parameters, smooth solutions of the shallow water equation converge to discontinuous solutions of a scalar conservation law...
متن کاملA Local Discontinuous Galerkin Method for the Camassa-Holm Equation
In this paper, we develop, analyze and test a local discontinuous Galerkin (LDG) method for solving the Camassa-Holm equation which contains nonlinear high order derivatives. The LDG method has the flexibility for arbitrary h and p adaptivity. We prove the L2 stability for general solutions and give a detailed error estimate for smooth solutions, and provide numerical simulation results for dif...
متن کاملGlobal Dissipative Solutions for the Two-component Camassa-holm Shallow Water System
This article presents a continuous semigroup of globally defined weak dissipative solutions for the two-component Camassa-Holm system. Such solutions are established by using a new approach based on characteristics a set of new variables overcoming the difficulties inherent in multi-component systems.
متن کامل