Related papers: On the generalized nonlinear Camassa-Holm equation
In this paper we consider a class of nonlinear wave equation with $x$-dependent coefficients and prove existence of families of time-periodic solutions under the general boundary conditions. Such a model arises from the forced vibrations of…
This paper deals with time stepping schemes for the Cahn--Hilliard equation with three different types of dynamic boundary conditions. The proposed schemes of first and second order are mass-conservative and energy-dissipative and -- as…
In this paper, we investigate the well-posedness of weak solutions to the time-fractional Fokker-Planck equation. Its dynamics is governed by anomalous diffusion, and we consider the most general case of space-time dependent forces.…
A family of Camassa-Holm type equations with a linear term and cubic and quartic nonlinearities is considered. Local well-posedness results are established via Kato's approach. Conserved quantities for the equation are determined and from…
In this paper, we study the control of the linear heat equation with a space and time dependent coefficient function by the Dirichlet and Neumann boundary control laws. This equation models the heat diffusion and space, time dependent heat…
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the…
In this article one will discuss the system of coupled nonlinear Klein-Gordon equations with different velocities and different masses. The nonlinearity considered is a general quadratic nonlinearity without any restriction. The method is a…
We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main features of these inequalities are that (a) they apply to a…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
In the present work, we focus on the space-time isogeometric discretization of a parabolic problem with a nonlocal diffusion coefficient. The existence and uniqueness of the solution for the continuous space-time variational formulation are…
We prove by using an iteration argument some blow-up results for a semilinear damped wave equation in generalized Einstein-de Sitter spacetime with a time-dependent coefficient for the damping term and power nonlinearity. Then, we…
In this paper we mainly investigate the periodic $\mu$-Camassa-Holm equation. We show the existence of global conservative solutions to the Cauchy problem of the periodic $\mu$-Camassa-Holm equation. The result is obtained by introducing a…
In this paper we prove global regularity for the full water waves system in 3 dimensions for small data, under the influence of both gravity and surface tension. This problem presents essential difficulties which were absent in all of the…
In this paper, we study the Cauchy problem for a generalized cross-coupled Camassa-Holm system with peakons and higher-order nonlinearities. By the transport equation theory and the classical Friedrichs regularization method, we obtain the…
This paper explores the solution of Fredholm-like equations with infinite dimensional solution spaces. We set out to find a method for determining a particular solution to a Fredholm-like equation subject to a given constraint. The…
In this paper we extend analysis of the WaveHoltz iteration -- a time-domain iterative method for the solution of the Helmholtz equation. We expand the previous analysis of energy conserving problems and prove convergence of the WaveHoltz…
This paper is concerned with the existence and uniqueness, and Ulam--Hyers stabilities of solutions of nonlinear impulsive $\varphi$--Hilfer fractional differential equations. Further, we investigate the dependence of the solution on the…
In this paper we examine the evolution of solutions, that initially have compact support, of a recently-derived system of cross-coupled Camassa-Holm equations. The analytical methods which we employ provide a full picture for the…
We consider time-dependent perturbations which are relatively bounded with respect to the square root of an unperturbed Hamiltonian operator, and whose commutator with the latter is controlled by the full perturbed Hamiltonian. The…
This paper is mainly concerned with the Cauchy problem for a generalized Camassa-Holm equation with analytic initial data. The analyticity of its solutions is proved in both variables, globally in space and locally in time. Then, we present…