On the blow-up of solutions in a class of strongly nonlinear Sobolev-type equationsстатья
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Дата последнего поиска статьи во внешних источниках: 2 октября 2014 г.
Аннотация:The Cauchy problem for abstract operator-differential equations of the form
Adudt+Lu=F(u)
is investigated.
The specified problem is quite well investigated in the case when A and L are linear operators, while the fully nonlinear case was an almost open question until now. Different partial differential equations of mathematical physics important for applications are particular cases of the above abstract equation; they are, e.g., strongly nonlinear third-order equations with the first-order derivative with respect to t (Sobolev-type equations), quasilinear equations of pseudoparabolic type, and the generalized Boussinesq-type equation with a nonlinear source.
The author finds the following two kinds of conditions for the operators A and L: (1)conditions providing the existence of a global (with respect to t) solution; (2)conditions providing the nonexistence of global (with respect to t) solutions. In the latter case, two-side estimates for the blow-up time are obtained.