| Conţinutul numărului revistei |
| Articolul precedent |
| Articolul urmator |
 581 0 |
 SM ISO690:2012PERJAN, Andrei, RUSU, Galina. Convergence estimates for abstract second order differential equations with two small parameters and monotone nonlinearities. In: Topological Methods in Nonlinear Analysis, 2019, nr. 2(54), pp. 1093-1110. ISSN 1230-3429. DOI: https://doi.org/10.12775/TMNA.2019.089 |
| EXPORT metadate: Google Scholar Crossref CERIF DataCite Dublin Core |
 Topological Methods in Nonlinear Analysis |
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| Numărul 2(54) / 2019 / ISSN 1230-3429 | ||||||
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| DOI:https://doi.org/10.12775/TMNA.2019.089 | ||||||
| Pag. 1093-1110 | ||||||
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In a real Hilbert space H we consider the following perturbed Cauchy problem [formula presented], where u0, u1 ∈ H, f: [0, T] ↦ H and ε, δ are two small parameters, A is a linear self-adjoint operator, B is a locally Lipschitz and monotone operator. We study the behavior of solutions uεδ to the problem (Pεδ) in two different cases: (i) when ε → 0 and δ ≥ δ0 > 0; (ii) when ε → 0 and δ → 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 neighborhood of t = 0. We show the boundary layer and boundary layer function in both cases. |
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| Cuvinte-cheie a priori estimate, Abstract second order, Cauchy problem, 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.I.</dc:creator> <dc:date>2019-12-25</dc:date> <dc:description xml:lang='en'><p>In a real Hilbert space H we consider the following perturbed Cauchy problem [formula presented], where u<sub>0</sub>, u<sub>1</sub> ∈ H, f: [0, T] ↦ H and ε, δ are two small parameters, A is a linear self-adjoint operator, B is a locally Lipschitz and monotone operator. We study the behavior of solutions u<sub>εδ</sub> to the problem (P<sub>εδ</sub>) in two different cases: (i) when ε → 0 and δ ≥ δ<sub>0</sub> > 0; (ii) when ε → 0 and δ → 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 neighborhood of t = 0. We show the boundary layer and boundary layer function in both cases.</p></dc:description> <dc:identifier>10.12775/TMNA.2019.089</dc:identifier> <dc:source>Topological Methods in Nonlinear Analysis 54 (2) 1093-1110</dc:source> <dc:subject>a priori estimate</dc:subject> <dc:subject>Abstract second order</dc:subject> <dc:subject>Cauchy problem</dc:subject> <dc:subject>boundary layer function</dc:subject> <dc:subject>singular perturbation</dc:subject> <dc:title>Convergence estimates for abstract second order differential equations with two small parameters and monotone nonlinearities</dc:title> <dc:type>info:eu-repo/semantics/article</dc:type> </oai_dc:dc>
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