Existence And Nonexistence Of Global Solutions For A Class Of 3 - D Strongly Damped Nonlinear Wave Equations

Infinite dimensional dynamical system is an important part of the nonlinear science, attractor is one of the core contents of the infinite dimensional dynamical system. Strongly damped nonlinear wave equation as an infinite dimensional dynamical system model, which is widely used in the field of chemical reaction theory, study physical phenomena and biological science research.This paper mainly studies the existence and nonexistence and global attractor of the global solutions for a class of strongly damped nonlinear wave equations.Among them, the number of β,η are positive constant; x∈Ω(?)R3, and Ω is a bounded domain with a smooth boundary, f(u) is a nonlinear function, g(x) is an external force.First of all, this paper use the Galerkin methods and some important inequalities, such as Holder inequality, Young inequality, Gronwall inequality, we prove the existence of the nonlinear function of the original function f(u) satisfies some conditions these problems the existence and uniqueness of global solutions and global attractors, and then prove the nonlinear function and initial function satisfies some conditions, the existence of global solution is not possible problems the initial value, the equation of the solutions blow up in finite time.The first part is the introduction, background and development overview of the related work;The second part introduces some of the concepts of strongly damped nonlinear wave equations and related knowledge;The third part proves the existence of the global attractor for the existence and global solutions under certain conditions of strongly damped nonlinear wave equations;The fourth part proves that does not exist solutions under some conditions.