In a real Hilbert space H we consider the following singularly perturbed Cauchy problem { εu′′ εδ (t) + δ u′ εδ (t) + Auεδ (t) + B(uεδ (t)) = f (t), t ∈ (0, T ), uεδ (0) = u0, u′ εδ (0) = u1, where u0, u1 ∈ H, f : ...

n a real Hilbert space H we consider the following perturbed Cauchy problem ( " u′′ " (t) + u′ " (t) + Au " (t) + B(u " (t)) = f(t), t ∈ (0, T ), u " (0) = u0, u′ " (0) = u1, (P " ) where u0, u1 ∈ H, f : [0, T ] 7→ H and ...

We study the existence of the limits of solutions to the semilinear plate equation with boundary Dirichlet condition with a small parameter coefficient of the second order derivative in time. We establish the convergence ...

We study the existence of the limits of solution to singularly perturbed initial boundary value problem of hyperbolic - parabolic type with boundary Dirichlet condition for the semilinear wave equation. We prove the ...

We study the behavior of solutions of the problem εu′′(t)+u′(t)+Au(t) =f (t), u(0) = u0, u′(0) = u1 in the Hilbert space H as ε → 0, where A is a linear,symmetric, strong positive operator.

We study the behavior of solutions to the problem(ε“u′′ε(t) +A1uε(t)”+u′ε(t) +A0uε(t) =f(t), t >0,uε(0) =u0, u′ε(0) =u1,in the Hilbert space H asε7→0, whereA1andA0are two linear selfadjoint operators.