Singular perturbation
β Scribed by J.D Cole
- Publisher
- Elsevier Science
- Year
- 1975
- Tongue
- English
- Weight
- 665 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0001-8708
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We consider a kind of singularly perturbed problem with a small positive parameter affecting the second order derivative only in a part of the domain. We analyse the existence and uniqueness of the solution and the asymptotic behaviour as the small parameter goes to zero.
Consider the equation Γe 2 Du e + q(x)u e = f(u e ) in R 3 , ju(1)j < 1, e = const > 0. Under what assumptions on q(x) and f(u) can one prove that the solution u e exists and lim e!0 u e = u(x), where u(x) solves the limiting problem q(x)u = f(u)? These are the questions discussed in the paper.
We study here singular perturbation problem for nonlinear difference equations with a small parameter. We consider analytic solutions for the systems and apply the theorem of boundary-layer corrections for singular perturbation problem for differential equations to the difference systems. We treat t