The analysis of the finite difference schemes with nonuniform meshes for the problems of partial differential equations is extremely rare even for very simple problems and even for the method of fully heuristic charac...
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The analysis of the finite difference schemes with nonuniform meshes for the problems of partial differential equations is extremely rare even for very simple problems and even for the method of fully heuristic character. In the present work the boundary value problem for quasilinear parabolic system is solved by the finite difference method with nonuniform meshes. By using of the interpolation formulas for the spaces of discrete functions with unequal meshsteps and the method of a priori estimation for the discrete solutions of finite difference schemes with nonuniform meshes, the absolute and relative convergence of the discrete solutions of the finite defference scheme are proved. The limiting vector function is just the unique generalized solution of the original problem for the parabolic system.
A kind of the general finite difference schemes with intrinsic parallelism for the boundary value problem of the quasilinear parabolic system is studied without assuming heuristically that the original boundary value ...
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A kind of the general finite difference schemes with intrinsic parallelism for the boundary value problem of the quasilinear parabolic system is studied without assuming heuristically that the original boundary value problem has the unique smooth vector solution. By the method of a priori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixed-point technique in finite dimensional Euclidean space, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general finite difference schemes with intrinsic parallelism is justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems in the discrete W 2 (2,1) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original quasilinear parabolic problem is proved.
In this paper the general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded coefficients are constructed, and the ex...
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In this paper the general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded coefficients are constructed, and the existence and uniqueness of the difference solution for the general schemes are proved. And the convergence of the solutions of the difference schemes to the generalized solution of the original boundary value problem of the semilinear parabolic system is obtained. The multidimensional problems are also studied.
In this paper, by using a priori estimates in the weighted space, the existence of the global attractor for the damped generalized coupled nonlinear wave equations in an unbounded domain is obtained.
In this paper, by using a priori estimates in the weighted space, the existence of the global attractor for the damped generalized coupled nonlinear wave equations in an unbounded domain is obtained.
This paper is concerned with the global existence and the partial regularity for the weak solution of the Landau-Lifshitz-Maxell system in two dimensions with Neumann boundary conditions.
This paper is concerned with the global existence and the partial regularity for the weak solution of the Landau-Lifshitz-Maxell system in two dimensions with Neumann boundary conditions.
Ferrimagnet is a kind of basic and important multi-sublattice magnet material. It has attracted more and more attention of physicists and mathematicians. Many results of solitons and numerical computations on this top...
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Ferrimagnet is a kind of basic and important multi-sublattice magnet material. It has attracted more and more attention of physicists and mathematicians. Many results of solitons and numerical computations on this topic have appeared. In this article, the dynamic equation for an isotropic ferrimagnet with two non-equivalent sublattices is studied, existence of weak solutions in multi dimension case is proved through the penalized method, the uniqueness and smoothness of the solution in one dimension case are also obtained by the relation between this equation and hyperbolic equation.
In this paper, the bifurcation method of dynamical systems and numerical approach of differential equations are employed to study CH-γ equation. Two new types of bounded waves are found. One of them is called the com...
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In this paper, the bifurcation method of dynamical systems and numerical approach of differential equations are employed to study CH-γ equation. Two new types of bounded waves are found. One of them is called the compacton. The other is called the generalized kink wave. Their planar graphs are simulated and their implicit expressions are given. The identity of theoretical derivation and numerical simulation is displayed.
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