This article is cited in 33 papers

Initial-boundary problem for parabolic-hyperbolic equation with loaded summands

K. B. Sabitov<sup>ab

a</sup> Laboratory of Differential Equations, Institute of Applied Research of Republic Bashkortostan, 68 Odesskaya str., Sterlitamak, 453103 Russia
^b Chair of Mathematics and Teaching Principles, Volga Region Social-Humanitarian Academy, 26 Antonov-Ovseenko str., Samara, 443090 Russia

Abstract: In the paper we find necessary and sufficient conditions for uniqueness of a solution to initial-boundary problem for a loaded equation of mixed parabolic-hyperbolic type. The solution is constructed in the form of sums of a series in eigenfunctions of the corresponding one-dimensional problem on eigenvalues. At a substantiation of convergence of series arises the problem of small denominators. Under certain conditions on these data we obtain an estimation of separation from scratch small denominator that has allowed to prove the existence theorem in the class of regular solutions.

Keywords: equation of mixed type with loaded summands, initial-boundary problem, uniqueness, existence, stability.

UDC: 517.956

Received: 17.01.2014

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:6, 23–33

Bibliographic databases:

•