Examples



mdbootstrap.com



 
Статья
2016

Positivity of solutions to inhomogeneous mixed-type equations of higher orders


K. B. SabitovK. B. Sabitov
Русская математика
https://doi.org/10.3103/S1066369X16030075
Abstract / Full Text

We study the solution to inhomogeneous mixed-type elliptic-hyperbolic equations of higher orders. We prove that the solution sign is constant and depends on the sign of the right-hand side of the equation.

Author information
  • Institute of Applied Research of Bashkortostan Republic, ul. Odesskaya 68, Sterlitamak, 453103, RussiaK. B. Sabitov
References
  1. Zhegalov, V. I. “A Boundary-Value Problem for Mixed-Type Equations of Higher Orders”, Dokl. Akad. Nauk SSSR 136, (2), 274–276 (1961).
  2. Bitsadze, A. V. Selected Papers (Nauka, Nal’chik, 2012).[in Russian].
  3. Agishev, R. Ya. “To the Problem of Mixed-Type Equations”, Trudy Kazansk. Aviats. Inst. 35, (3), 3–10 (1957).
  4. Tikhonov, A. N. and Samarskii, A. A. Equations of Mathematical Physics (Nauka, Moscow, 1960).[in Russian].
  5. Muskhelishvili, N. I. Fundamental Problems in the Theory of Elasticity (Nauka, Moscow, 1966).[in Russian].
  6. Sobolev, S. L. Introduction to the Theory of Cubature Formulas (Nauka, Moscow, 1974).[in Russian].
  7. Petrovskii, I. G. Lectures on Partial Differential Equations (Gostekhizdat, Moscow–Leningrad, 1950).[in Russian].
  8. Sabitov, K. B. Equations ofMathematical Physics (Fizmatlit, Moscow, 2013).[in Russian].
  9. Sabitov, K. B. “Construction in Explicit Form of the Solutions of the Darboux Problem for the Telegraph Equation and Thier Application to the Treatment of Integral Equations”, Differ. Equations 26, No. 6, 747–755 (1990).