Conţinutul numărului revistei |
Articolul precedent |
Articolul urmator |
210 0 |
SM ISO690:2012 PERJAN, Andrei, RUSU, Galina. Convergence estimates for some abstract linear second order differential equations with two small parameters. In: Asymptotic Analysis, 2016, vol. 97, pp. 337-349. ISSN 0921-7134. DOI: https://doi.org/10.3233/ASY-161357 |
EXPORT metadate: Google Scholar Crossref CERIF DataCite Dublin Core |
Asymptotic Analysis | ||||||
Volumul 97 / 2016 / ISSN 0921-7134 /ISSNe 1875-8576 | ||||||
|
||||||
DOI:https://doi.org/10.3233/ASY-161357 | ||||||
Pag. 337-349 | ||||||
|
||||||
Descarcă PDF | ||||||
Rezumat | ||||||
In a real Hilbert space H we consider the following singularly perturbed Cauchy problem (Equation presented) where u0, u1 ∈ H, f : [0, T ] → H and ϵ, δ are two small parameters. We study the behavior of the 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 a priori estimates of the solutions to the perturbed problem, which are uniform with respect to the parameters, and a relationship between the solutions to both problems. We establish that the solution to the unperturbed problem has a singular behavior with respect to the parameters in the neighborhood of t = 0. We describe the boundary layer and the boundary layer function in both cases. |
||||||
Cuvinte-cheie a priori estimate, abstract second order Cauchy problem, boundary layer function, singular perturbation |
||||||
|