The conditions of existence of a solution of the degenerate two-point in time problem for PDE-Reference-Cited by-同舟云学术

The conditions of existence of a solution of the degenerate two-point in time problem for PDE

Published:2019-05-27 Issue:03 Volume:12 Page:1950037
ISSN:1793-5571
Container-title:Asian-European Journal of Mathematics
language:en
Short-container-title:Asian-European J. Math.

Author:

Nytrebych Zinovii¹,Malanchuk Oksana¹²

Affiliation:

1. Department of Mathematics, Lviv Polytechnic National University, 12 Bandery Str., Lviv 79013, Ukraine

2. Department of Biophysics, Danylo Halytsky Lviv National Medical University, 69, Pekarska Str., Lviv 79017, Ukraine

Abstract

The problem with local nonhomogeneous two-point in time conditions for homogeneous PDE of the second order in time and, generally, infinite order in spatial variables is investigated. This problem is degenerated namely its characteristic determinant is identically zero. The condition of existence of a solution of the degenerate problem is established. Also, we proposed the differential-symbol method of constructing the solution of the problem in the classes of entire functions. Some examples of solving the degenerate two-point in time problems are presented.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793557119500372

Reference14 articles.

1. Problem with nonlocal two-point condition in time for a homogeneous partial differential equation of infinite order with respect to space variables

2. An investigation into a problem with homogeneous local two-point conditions for a homogeneous system of partial differential equations

3. On an operational method of solving initial-value problems for partial differential equations induced by generalized separation of variables

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