| Conţinutul numărului revistei |
| Articolul precedent |
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 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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| Rezumat | ||||||
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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