TY - JOUR
T1 - Life-span of solutions to nonlinear dissipative evolution equations
T2 - A singular perturbation approach
AU - Milani, Albert
N1 - Publisher Copyright:
© 2000 EUT Edizioni Universita di Trieste.
PY - 2000
Y1 - 2000
N2 - 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.
AB - 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.
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M3 - Article
AN - SCOPUS:85046705846
SN - 0049-4704
VL - 31
SP - 189
EP - 208
JO - Rendiconti dell'Istituto di Matematica dell'Universita di Trieste
JF - Rendiconti dell'Istituto di Matematica dell'Universita di Trieste
ER -