Different convergences in approximation of evolution equations
Küçük Resim Yok
Tarih
2009
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
Consider the semilinear equation in Banach space E ? u 0 (t) = Au(t) + f(u(t)), t ? 0, u(0) = u 0 ? E ?, (0.1) where f(·) : E ? ? E ? E, 0 ? ? < 1, is assumed to be continuous, bounded and continuously Fr´echet differentiable function. The problem (0.1) in the neighborhood of the hyperbolic equilibrium can be written in the form, where Au? = A+f 0 (u ? ), Fu? (v(t)) = f(v(t)+u ? )?f(u ? )?f 0 (u ? )v(t). We consider approximation of (0.2) by the following scheme, with initial data Vn(0) = v 0 n. The solution of such problem is given by formula Vn(t + ?n) = (In ? ?nAu? n,n) ?1Vn(t) + ?n(In ? ?nAu? n,n) ?1Fu? n,n(Vn(t)) = = (In ? ?nAu? n,n) ?kVn(0) + ?n? k j=0(In ? ?nAu? n,n) ?(k?j+1)Fu? n,n(Vn(j?n)), t = k?n, where Vn(0) = v 0 n. We consider different kind of consistency of generators under which one can get convergence of solutions in the vicinity of hyperbolic stationary point.
Açıklama
Anahtar Kelimeler
Kaynak
International Conference of Mathematical Sciences
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Piskarev, S. (2009). Different convergences in approximation of evolution equations. Maltepe Üniversitesi. s. 352.
