We investigate the large time behavior of solutions to nonlinear dissipative wave equations of the general form εuu + ut - Δu = F(x, t, u, Dxu, Dx2u); in particular, we study the dependence of the solutions u = uε and of their life span Tε on the (small) parameter ε. We are interested in the behavior of uε and Tε as ε → 0, and in their relations with the solution v, and its life span Tp, of the corresponding limit equation when ε = 0, which is of parabolic type. We look for conditions under which either Tε = +∞, or Tε → Tp < +∞ as ε → 0.
|Number of pages||20|
|Journal||Rendiconti dell'Istituto di Matematica dell'Universita di Trieste|
|Publication status||Published - 2000|
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