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Global well -posedness for systems of nonlinear wave equations
This dissertation deals with the global well-posedness of the system of nonlinear wave equations utt-Du+&parl0;du k+evl&parr0; utm-1u t=f1u,v utt-Dv+&parl0;d′ uq+ e′ur &parr0;vt r-1vt=f2u,v , in a bounded domain Ω ⊂ Rn , n = 1, 2, 3; with Dirichlét boundary conditions. The nonlinearities f1(u, v) and f2(u, v) act as a strong source in the system and the exponents of velocities are restricted to the range 0 < m, r ≤ 1. The non-critical case 0 < m, r < 1 and the critical case m = r = 1 are analyzed in Chapter 2 and Chapter 3, respectively. Under some restrictions on the parameters in the system we obtain several results on the existence of local solutions, global solutions, and uniqueness. In addition, we prove that weak solutions to the system blow up in finite time whenever the initial energy is negative and the exponent the source term is more dominant than the exponents of both damping terms.^
Sakuntasathien, Sawanya, "Global well -posedness for systems of nonlinear wave equations" (2008). ETD collection for University of Nebraska - Lincoln. AAI3297658.