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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 | |||||||
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Pag. 233-246 | |||||||
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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 uεδ 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. |
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Cuvinte-cheie A priory estimate, boundary layer function, singular perturbation |
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Dublin Core Export
<?xml version='1.0' encoding='utf-8'?> <oai_dc:dc xmlns:dc='http://purl.org/dc/elements/1.1/' xmlns:oai_dc='http://www.openarchives.org/OAI/2.0/oai_dc/' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xsi:schemaLocation='http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd'> <dc:creator>Perjan, A.</dc:creator> <dc:creator>Rusu, G.</dc:creator> <dc:date>2017-04-10</dc:date> <dc:description xml:lang='en'><p>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, u<sub>0</sub>, u<sub>1</sub> ∈ H, f: [0, T ] ↦→ H and ε, δ are two small parameters. We study the behavior of solutions u<sub>εδ</sub> to this problem in two different cases: ε → 0 and δ ≥ δ<sub>0</sub> > 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.</p></dc:description> <dc:source>Carpathian Journal of Mathematics () 233-246</dc:source> <dc:subject>A priory estimate</dc:subject> <dc:subject>boundary layer function</dc:subject> <dc:subject>singular perturbation</dc:subject> <dc:title>Abstract linear second order differential equations with two small parameters and depending on time operators</dc:title> <dc:type>info:eu-repo/semantics/article</dc:type> </oai_dc:dc>