Dissertation > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems

Strongly damped nonlinear wave equation with initial boundary value problem

Author MaTengYu
Tutor LiuYaCheng
School Harbin Engineering University
Course Applied Mathematics
Keywords Potential well tribe Nonlinear wave equation Existence of Global Solutions Vacuum isolation Asymptotic behavior
CLC O175.8
Type Master's thesis
Year 2008
Downloads 43
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In this paper, we study any strong damping term dimensions the initial-boundary value problem of nonlinear wave equation u < sub > tt < / sub > alpha delta u < sub > t < / sub > - delta u = f (u), x ∈ Ω u = u (x, 0) < sub > 0 < / sub > (x), u < sub > t < / sub >, (x, 0) = u < sub > 1 < / sub > (x), x ∈ Ω u | (?,?,?,?,?) Ω = 0 which Ω (?,?,?,?,?) R < sup > n < / sup > for appropriate smooth boundaries. First of all, we applied the new method introduced one new potential Wells, and then the family of new potential Wells method is applied to get the global solution of the problem of the existence theorem and the related reasoning, and then proves the existence of weak solutions whole, whole existence and uniqueness of strong solutions; Secondly, study the problem of the invariant sets and vacuum isolating phenomena. Finally, using the improved integral estimation method, under the presumption of nonlinear term is very broad, prove strong overall solution when time t - up exponentially asymptotic properties of decay to zero.

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