A NOTE ON “THE CAUCHY PROBLEM FOR COUPLED IMBQ EQUATIONS”

doi:10.1016/S0252-9602(13)60005-3

Abstract

Abstract:

In this article, we prove that the Cauchy problem for a N-dimensional system of nonlinear wave equations
u_tt − aΔu_tt = Δf(u, v), x ∈ R^N, t > 0,
v_tt − aΔv_tt = Δg(u, v), x ∈ R^N, t > 0
admits a unique global generalized solution in C³([0, ∞); W ^{m, p}(R^N) ∩L^∞(R^N)∩L²(R^N))(m ≥ 0 is an integer, 1 ≤ p < 1 ) and a unique global classical solution in C³([0, ∞); W ^m,p∩L^∞ ∩L²) (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.

Key words: N-dimensional system of nonlinear wave equations, Cauchy problem, global solution, blow up of solution

CLC Number:

35L30

GUO Hong-Xia, CHEN Guo-Wang. A NOTE ON “THE CAUCHY PROBLEM FOR COUPLED IMBQ EQUATIONS”[J].Acta mathematica scientia,Series B, 2013, 33(2): 375-392.

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