Singularly perturbed problems of hyperbolic-parabolic type with lipschitzian nonlinearity

• Published in: Нелинейные граничные задачи
• Date: 2005
• Main Author: Perjan, A.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2005
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/169157
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Singularly perturbed problems of hyperbolic-parabolic type with lipschitzian nonlinearity / A. Perjan // Нелинейные граничные задачи. — 2005. — Т. 15. — С. 99-107. — Бібліогр.: 4 назв. — англ.

We study the behavior of solutions of the Cauchy problem εu"(t)+u'(t) + Au(t)+B(u(t)) = f(t), u(0) = u₀, u'(0) = u₁ in the Hilbert space H as ε → 0, where A is a linear, self-adjoint, strong positive operator B is nonlinear Lipschitzian operator.