A Boundary Value Problem for a Mixed Type Equation in a Cylindrical Domain
- Authors: Artyushin A.N.1
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Affiliations:
- Sobolev Institute of Mathematics
- Issue: Vol 60, No 2 (2019)
- Pages: 209-222
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172299
- DOI: https://doi.org/10.1134/S0037446619020034
- ID: 172299
Cite item
Abstract
We examine a boundary value problem for a mixed type equation of the second order in a cylindrical domain. Under certain conditions, the existence of regular solutions in a suitable weighted Sobolev space is proven by regularization. The uniqueness of solutions is also established under the same conditions. A few estimates of the second derivatives of a generalized solution are obtained in the elliptic-parabolic domain.
About the authors
A. N. Artyushin
Sobolev Institute of Mathematics
Author for correspondence.
Email: alexsp3@yandex.ru
Russian Federation, Novosibirsk