Skip to main content
padlock icon - secure page this page is secure

Asymptotic Expansions for Two Singularly Perturbed Convection–Diffusion Problems with Discontinuous Data: The Quarter Plane and the Infinite Strip

Buy Article:

$59.00 + tax (Refund Policy)

We consider a singularly perturbed convection–diffusion equation, , defined on two domains: a quarter plane, (x, y) ∈ (0, ∞) × (0, ∞) , and an infinite strip, (x, y) ∈ (−∞, ∞) × (0, 1) . We consider for both problems discontinuous Dirichlet boundary conditions: u(x, 0) = 0 and u(0, y) = 1 for the first one and u(x, 0) =[a,b](x) and u(x, 1) = 0 for the second. For each problem, asymptotic expansions of the solution are obtained from an integral representation in two limits: (a) when the singular parameter → 0+ (with fixed distance r to the discontinuity points of the boundary condition) and (b) when that distance r→ 0+ (with fixed ). It is shown that in both problems, the first term of the expansion at = 0 is an error function or a combination of error functions. This term characterizes the effect of the discontinuities on the -behavior of the solution and its derivatives in the boundary or internal layers. On the other hand, near the discontinuities of the boundary condition, the solution u(x, y) of both problems is approximated by a linear function of the polar angle at the discontinuity points.
No References
No Citations
No Supplementary Data
No Article Media
No Metrics

Document Type: Research Article

Publication date: July 1, 2004

  • Access Key
  • Free content
  • Partial Free content
  • New content
  • Open access content
  • Partial Open access content
  • Subscribed content
  • Partial Subscribed content
  • Free trial content
Cookie Policy
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more