Facultatea de Matematică şi Informatică / Faculty of Methematics and Informatics
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Item LIMITS OF SOLUTIONS TO THE SEMILINEAR PLATE EQUATION WITH SMALL PARAMETER(Academia de Ştiinţe a Moldovei, 2022) Perjan, Andrei; Rusu, GalinaWe 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 of solutions to the perturbed problem and their derivatives in spacial variables to the corresponding solutions to the unperturbed problem as the small parameter tends to zero.Item CONVERGENCE ESTIMATES FOR SOME ABSTRACT SECOND ORDER DIFFERENTIAL EQUATIONS IN HILBERT SPACES("VALINEX", 2019-09-28) Perjan, Andrei; Rusu, Galinan 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 ", are two small parameters, A is a linear self-adjoint operator, B is a locally Lipschitz and monotone operator. We study the behavior of solutions u " to the problem (P " ) in two different cases: (i) when " → 0 and ≥ 0 > 0; (ii) when " → 0 and → 0. We establish that the solution to the unperturbed problem has a singular behavior, relative to the parameters, in the neighborhood of t = 0. We show the boundary layer and boundary layer function in both cases.Item TWO PARAMETER SINGULAR PERTURBATION PROBLEMS FOR SINE-GORDON TYPE EQUATIONS(2022) Perjan, Andrei; Rusu, GalinaIn the real Sobolev space H1 0 (Ω) we consider the Cauchy-Dirichlet problem for sine-Gordon type equation with strongly elliptic operators and two small parameters. Using some a priori estimates of solutions to the perturbed problem and a relationship between solutions in the linear case, we establish convergence estimates for the difference of solutions to the perturbed and corresponding unperturbed problems. We obtain that the solution to the perturbed problem has a singular behavior, relative to the parameters, in the neighbourhood of t = 0Item LIMITS OF SOLUTIONS TO THE SINGULARLY PERTURBED ABSTRACT HYPERBOLIC-PARABOLIC SYSTEM(2014) Perjan, Andrei; Rusu, GalinaWe study the behavior of solutions to the problem εu′′ε(t) +u′ε(t) +A(t)uε(t) =fε(t), t∈(0, T), uε(0) =u0ε, u′ε(0) =u1ε,in the Hilbert space H asε→0, whereA(t), t∈(0,∞),is a family of linear self-adjoint