Abstract linear second order differential equations with two small parameters and depending on time operators

Perjan Andrei; Rusu Galina

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651

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2018-10-28 00:44

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PERJAN, Andrei, RUSU, Galina. Abstract linear second order differential equations with two small parameters and depending on time operators. In: Carpathian Journal of Mathematics, 2017, vol. 33, pp. 233-246. ISSN 1584-2851.

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Carpathian Journal of Mathematics

Volumul 33 / 2017 / ISSN 1584-2851 /ISSNe 1843-4401

Abstract linear second order differential equations with two small parameters and depending on time operators

Pag. 233-246

Perjan Andrei, Rusu Galina

Moldova State University

Proiecte:

20.80009.5007.05 Nanoparticule metalice biofuncționalizate - obținerea cu ajutorul cianobacteriilor și microalgelor

Disponibil în IBN: 28 iunie 2018

Rezumat

In a real Hilbert space H consider the following singularly perturbed Cauchy problem (Formula presented), where A(t): V ⊂ H → H, t ∈ [0, ∞), is a family of linear self-adjoint operators, u₀, u₁ ∈ H, f: [0, T ] ↦→ H and ε, δ are two small parameters. We study the behavior of solutions u_εδ to this problem 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 perturbed 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.

Cuvinte-cheie
A priory estimate, boundary layer function, singular perturbation

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