The Existence And Uniqueness Of Solutions For A Generalized Nonlinear Sine-Gordon Equation With Strong Damping

At present, with the development of practical problems and some other sciences on the one hand, and with the advancement of mathematics itself on the other, the research on infinite-dimensional dynamics systems has become one of the important subjects of dynamic systems. The research of the limited-dimensional dynamic systems of the dynamics systems there has been 30 years' history at least, and obtain many important results. But the problem of the dynamics systems does not be limited by the circumstance of the limited-dimensional far and far. we have discovered a large quantity nonlinear evolution equation with soliton, For example kdv equation, nonlinear Schrodinger equation, Zakharov equation etc, under the function of dissipation evolve from the soliton to chaos, in addition, some dissipation partial differential equations, such as: reaction-diffusion equation, Navier-stokes equation, Kuramoto-Sivashinskey equation etc, has similar phenomen -on. The research on infinite-dimensional dynamics systems is already...