Dirichlet’s problem for a third-order parabolic hyperbolic type equation of the second kind

Equations of mixed type, the degeneracy line of which is the envelope of a family of characteristics, therefore, is itself also a characteristic, in the literature it is customary to call equations of mixed type of the second kind, which causes additional difficulties in the study of boundary value...

Full description

Saved in:
Bibliographic Details
Published inE3S web of conferences Vol. 401; p. 3049
Main Authors Abdullaev, A. A., Xolbekov, J. A., Axralov, H.
Format Journal Article
LanguageEnglish
Published EDP Sciences 01.01.2023
Online AccessGet full text

Cover

More Information
Summary:Equations of mixed type, the degeneracy line of which is the envelope of a family of characteristics, therefore, is itself also a characteristic, in the literature it is customary to call equations of mixed type of the second kind, which causes additional difficulties in the study of boundary value problems for equations of the second kind. In the present work, a boundary value problem for a homogeneous equation of parabolic-hyperbolic type of the third order of the second kind is investigated. Necessary and sufficient conditions for the existence and uniqueness of a generalized solution of the problem are found. In some special cases, the representation of the solution of the problem under study is written out explicitly.
ISSN:2267-1242
2267-1242
DOI:10.1051/e3sconf/202340103049