Local existence and global nonexistence theorems for a damped nonlinear hyperbolic equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:368

Article

Chen, Guowang¹  Song, Ruili²  Wang, Shubin¹ 

[1] Zhengzhou Univ, Dept Mat, Zhengzhou 450052, Peoples R China

[2] Zhongyuan Univ Technol, Coll Informat & Business, Zhengzhou 450007, Peoples R China

关键词: Damped nonlinear hyperbolic equation;    Initial boundary value problem;    Local solution;    Blow up of solutions;   

DOI  :  10.1016/j.jmaa.2010.02.054

来源: Elsevier

【 摘 要 】

The existence and uniqueness of the local generalized solution to the initial boundary value problem for the three-dimensional damped nonlinear hyperbolic equation u(tt) + k(1)del(4)u + k(2)del(4)ut + del(2)g(del(2)u) = 0, (x, t) is an element of Omega x (0, T), u = 0, del(2)u = 0, (x, t) is an element of partial derivative Omega x (0, T), u(x, 0) = u(0)(x), u(t)(x, 0) = u(1)(x), x is an element of Omega subset of R(3) are proved. The paper arrives at some sufficient conditions for blow up of the solutions in finite time by two methods. An example is given. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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