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Blow-up of solutions of abstract Cauchy problems for nonlinear operator-differential equationsстатья
- Авторы: Korpusov M.O., Sveshnikov A.G.
- Журнал: Dokl. Akad. Nauk (Russ.)
- Том: 401
- Номер: 1
- Год издания: 2005
- Первая страница: 12
- Последняя страница: 15
- Аннотация: This paper deals with the global existence of the weak solutions to the abstract Cauchy problem for three kinds of nonlinear operator-differential equations, such as, e.g., ddt(A0u+∑j=1NAj(u))=F(u),ddt(A0u+∑j=1NAj(u))+Lu=F(u),ddt(A0u+∑j=1NAj(u))+D(P(u))=F(u), with the Cauchy datum u(0)=u0. The authors state that by applying Galerkin's method combined with monotonicity and compactness methods, they obtain several results on the global existence and the blow-up of the solutions for these problems (no proofs are given in the paper). As applications of the results, the authors give some examples, such as, e.g., ∂∂t(Δu+∑j=1ndiv(|∇u|pj−2∇u))+|u|qu=0,(x,t)∈Ω×[0,T], u=0on ∂Ω,u(x,0)=u0(x)for x∈Ω.
- Добавил в систему: Корпусов Максим Олегович