Facultatea de Matematică şi Informatică / Faculty of Methematics and Informatics
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Item LIMITS OF SOLUTIONS TO THE SEMILINEAR WAVE EQUATION WITH SMALL PARAMETER(Academia de Ştiinţe a Moldovei, 2006) Perjan, AndreiWe 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 convergence of solutions and also the convergence of gradients of solutions to perturbed problem to the corresponding solutions to the unperturbed problem as the small parameter tends to zero. We show that the derivatives of solution relative to time-variable possess the boundary layer function of the exponential type in the neighborhood of t = 0Item LINEAR SINGULAR PERTURBATIONS OF HYPERBOLIC-PARABOLIC TYPE(Academia de Ştiinţe a Moldovei, 2003) Perjan, AndreiWe 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.Item SINGULAR PERTURBATIONS OFHYPERBOLIC-PARABOLIC TYPE(Institutul de Matematică şi Informatică al AŞM, 2003) Perjan, AndreiWe study the behavior of solutions of the problemεu′′(t)+u′(t)+Au(t) =f(t), u(0) =u0, u′(0) =u1in the Hilbert spaceHasε→0, whereAis a linear,symmetric, strong positive operator.