Limits of the Solutions to the Initial-Boundary Dirichlet Problem for the Semilinear Klein-Gordon Equation with Two Small Parameters

Perjan Andrei; Rusu Galina

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PERJAN, Andrei, RUSU, Galina. Limits of the Solutions to the Initial-Boundary Dirichlet Problem for the Semilinear Klein-Gordon Equation with Two Small Parameters. In: Conference on Applied and Industrial Mathematics: CAIM 2018, 20-22 septembrie 2018, Iași, România. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2018, Ediţia a 26-a, p. 64. ISBN 978-9975-76-247-2.

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Conference on Applied and Industrial Mathematics
Ediţia a 26-a, 2018

Conferința "Conference on Applied and Industrial Mathematics"
Iași, România, Romania, 20-22 septembrie 2018

Limits of the Solutions to the Initial-Boundary Dirichlet Problem for the Semilinear Klein-Gordon Equation with Two Small Parameters

Pag. 64-64

Perjan Andrei, Rusu Galina

Moldova State University

Disponibil în IBN: 1 iunie 2022

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We study the behavior of solutions u" to the problem (P") in two di erent cases: (i) when " ! 0 and 0 > 0; (ii) when " ! 0 and ! 0: 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 = 0: We show the boundary layer and boundary layer function in both cases.

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