IJPAM: Volume 113, No. 4 (2017)

Title

THE CAUCHY PROBLEM FOR
THE MC KENDRICK-VON FOERSTER LOADED EQUATION

Authors

Anatoly Kh. Attaev
Institute of Applied Mathematics and Automation
RUSSIA

Abstract

We study the Cauchy problem for equations of type $u_x+u_t+c\,u=\lambda u(x_0,t)$ with initial value given in a characteristic and a non-characteristic manifolds. Necessary conditions for the existence and uniqueness of the solution are found, and their explicit analytical representations are given.

History

Received: December 15, 2016
Revised: January 30, 2017
Published: March 30, 2017

AMS Classification, Key Words

AMS Subject Classification: 35F10
Key Words and Phrases: Cauchy problem, loaded equation, infuence domain, definition domain, dependence domain

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
A.M. Nakhushev, The equation of mathematical biology, Vysshayashkola, Moscow (1995).

2
A.M. Nakhushev, Loaded equations and their applications, Nauka, Moscow (2012).

3
A.V. Bitsadze, Equations of mathematical physics, Nauka, Moscow (1982).

4
I.S. Lomov, Loaded Differential Operators: convergence of spectral expansions,Differential Equations, 191, (1983), 86-94.

5
A.M. Nakhushev, On the Darboux problem for a degenerate second order integroloaded equations,Differential Equations, 12, (1976), 103-108.

6
M.T. Dzhenaliev, Boundary value problems for the loaded parabolic and hyperbolic equations with time derivative in boundary conditions,Differential Equations, 30, (1994), 723-724.

7
M.T. Dzhenaliev, M.I. Ramazanov, On the solvability of boundary value problems for the loaded equations,Mathematical Journal, 1, (2001), 21-29.

8
A.Kh. Attaev, The characteristic Cauchy problem for linear loaded hyperbolic equation,Reports of the Adyghe (Circassian) International Academy ofSciences, 15, (2013), 9-12.

9
A.Kh. Attaev, The problem with data on parallel characteristics for the loaded wave equation,Reports of the Adyghe (Circassian) International Academy ofSciences, 15, (2013), 25-28.

10
A.Kh. Attaev, The Cauchy problem for the Mc Kendrick-Von Foersterloaded equation, Kazakh Mathematical Journal, 17,No. 1 (2017), 28.

How to Cite?

DOI: 10.12732/ijpam.v113i4.5 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 4
Pages: 47 - 52


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).