A NOTE ON "THE CAUCHY PROBLEM FOR COUPLED IMBQ EQUATIONS"

作者：Guo Hongxia^*; Chen Guowang

来源：Acta Mathematica Scientia, 2013, 33(2): 375-392.

DOI：10.1016/s0252-9602(13)60005-3

• N-dimensional system of nonlinear wave equations
• Cauchy problem
• global solution
• blow up of solution

In this article, we prove that the Cauchy problem for a N-dimensional system of nonlinear wave equations
u(tt) - alpha Delta u(tt) = Delta f(u, v), x is an element of R-N, t > 0,
v(tt) - alpha Delta v(tt) = Delta g(u, v), x is an element of R-N, t > 0
admits a unique global generalized solution in C-3([0, infinity); W-m,W-p (R-N) boolean AND L-infinity (R-N) boolean AND L-2 (R-N)) (m >= 0 is an integer, 1 <= p <= infinity) and a unique global classical solution in C-3([0, infinity); W-m,W-p boolean AND L-infinity boolean AND L-2) (m > 2 + N/P), the sufficient conditions of the blow up of the solution in finite time are given, and also two examples are given.

• 出版日期2013-3
• 单位郑州大学