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- Title
Application of the Hausdorff Metric in Model Problems with Discontinuous Functions in Boundary Conditions.
- Authors
Kostin, A. B.; Sherstyukov, V. B.
- Abstract
Using an example of the Cauchy problem for the one-dimensional heat equation, we study the approximation of the solution to the initial condition in the Hausdorff metric. The simplest discontinuous function u0(x) = sgn x is taken for the initial condition. Based on the asymptotic behavior of the Lambert W function and its modification, we obtain a two-sided estimate and an asymptotics for the Hausdorff distance between the solution given by the Poisson formula and the function u0(x). Similar results are obtained for a similar model problem for the Laplace equation in the upper half-plane.
- Subjects
DISCONTINUOUS functions; HEAT equation
- Publication
Journal of Mathematical Sciences, 2023, Vol 274, Issue 4, p511
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-023-06616-6