On a non-standard conjugation problem for elliptic equations

  • Kozhanov Alexander I., kozhanov@math.nsc.ru Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk 630090, Russia; Novosibirsk State University, 2 Pirogov Street, 2, Novosibirsk 630090, Russia
  • Potapova Sargylana V., sargyp@inbox.ru M. K. Ammosov Nord-Eastern Federal University, Research Institute of Mathematic, Kulakovskogo st., 48, Yakutsk 677000, Russia
Keywords: conjugation problem, regular solution, sewing condition, elliptic equation, discontinuous boundary conditions

Abstract

We investigate the regular solvability of the conjugation problem for elliptic equations with non-standard boundary conditions and sewing conditions on the plane $x = 0$. Let $Q$ be a parallelepiped. On the bottom of $Q$ we give a boundary condition for $u(x, t, a)$ in the part where $x>0$ and for $u_t(x, t, a)$ in the part where $x<0$. On the plane $x=0$ these conditions "intertwist", so on the top of $Q$ we give a boundary condition for $u(x, t, a)$ in the part where $x<0$ and for $u_t(x, t, a)$ in the part where $x > 0$. Combining the regularization method and natural parameter continuation, we prove the uniqueness and existence theorems for regular solutions of this non-standard conjugation problem.

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How to Cite
Kozhanov, A. and Potapova, S. (2016) “On a non-standard conjugation problem for elliptic equations”, Mathematical notes of NEFU, 23(3), pp. 70-80. Available at: http://mzsvfu.ru/index.php/mz/article/view/on-a-non-standard-conjugation-problem-for-elliptic-equations (Accessed: 22September2020).
Section
Mathematics