2. Articole
Permanent URI for this collectionhttps://msuir.usm.md/handle/123456789/17
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Item LIMITS OF SOLUTIONS TO THE SEMILINEAR PLATE EQUATION WITH SMALL PARAMETER(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 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 ABSTRACT SECOND ORDER DIFFERENTIAL EQUATIONS WITH TWO SMALL PARAMETERS AND LIPSCHITZIAN NONLINEARITIES(Centrul Universitar Nord din Baia Mare, 2022) Perjan, Andrei; Rusu, GalinaIn 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 : [0, T ] 7 → H, ε, δ are two small parameters, A is a linear self-adjoint operator and B is a nonlinear A1/2 Lipschitzian operator. We study the behavior of solutions uεδ in two different cases: ε → 0 and δ ≥ δ0 > 0; ε → 0 and δ → 0, relative to solution to the corresponding unperturbed problem. We obtain some a priori estimates of solutions to the perturbed problem, which are uniform with respect to parameters, and a relationship between solutions to both problems. We establish that the solution to the unperturbed problem has a singular behavior, relative to the parameters, in the neighbourhood of t = 0Item 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 = 0