Asymptotic Solutions of the Dirichlet Problem for the Heat Equation at a Characteristic Point

• Date: 2014
• Main Authors: Antoniouk, A. Vict., Kiselev, O. M., Tarkhanov, N. N., Антонюк, О. Вік., Кисельов, О. М., Тарханов, Н. Н.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2014
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2223
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

The Dirichlet problem for the heat equation in a bounded domain $G ⊂ ℝ^{n+1}$ is characteristic because there are boundary points at which the boundary touches a characteristic hyperplane $t = c$, where c is a constant. For the first time, necessary and sufficient conditions on the boundary guarante...