Singularly perturbed problems of hyperbolic-parabolic type with lipschitzian nonlinearity - Perjan, A. (Нелинейные граничные задачи, 2005)
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.