Note Of Global Solution For Two Class Of Nonlinear Parabolic Equation And Wave Equation

By the test function method, in this paper, we deal with a kind of degenerate parabolic problems. The global nonexistence of nontrivial solutions for some degenerate parabolic equation and inequalities, with nonlocal term are contained. Together with the existence and the nonexistence, the uniqueness and the energy decay of solution for the fourth-order nonlinear wave equation are considered in this paper..The main content of this paper is divided into three Chapters.In Chapter 2, we concerned with the nonexistence questions for the global nontrivial solutions to the degenerate parabolic inequalities which involving local and nonlocal termsandWhere n, m, p, q > 0, N > 2, β(y) is a nonnegative measurable functions in R ~N .In Chapter 3, we are concerned with nonexistence of nonnegative nontrivial solution to the degenerate parabolic equation with nonlocal termWhere Ω is unbounded cone domain in R~N . Some sufficient conditions on the global nonexistence results are obtained.In chapter 4, the existence and the nonexistence, the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equationare studied. .The existence of the solution is gotten by the Galekin approximation method. The energy decay rate of the global solution is estimated by the multiplier method. The blow-up result of the solution in finite time is established by the ideal of a potential well theory.