Address: Vatutina st. 53, Vladikavkaz,
362025, RNO-A, Russia
Phone: (8672)23-00-54
E-mail: rio@smath.ru
Dear authors!
Submission of all materials is carried out only electronically through Online Submission System in
personal account.
DOI: 10.23671/VNC.2016.4.5997
A Maximum Principle for a Loaded Hyperbolic-Parabolic Equation
Khubiev K. U.
Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 4.
Abstract: We prove the maximum principle for a loaded equation of hyperbolic-parabolic type with variable coefficients. The characteristic load term is given on the degenerate line. The obtained results generalize the maximum principle for hyperbolic-parabolic equations provided in T. D. Dzhuraev's monograph, and in the hyperbolic domain the well-known Agmon-Nirenberg-Protter principle.
Keywords: maximum principle, loaded equation, equation of mixed type, hyperbolic-parabolic equation
1. Nakhushev A. M. Nagruzhennye uravneniya i ikh primeneniya [Loaded
Equations and Its Application]. Moscow, Nauka, 2012. 232 p.
2. Bitsadze A. V. On Some Problems of Mixed Type. Dokl. Akad. Nauk
SSSR [Soviet Mathematics. Doklady], 1950, vol. 70, no. 4, pp.561-565
[in Russian].
3. Sabitov K. B. The Maximum Principle for Equations of Mixed Type.
Differential Equations, 1989, vol. 24, no. 11, pp. 1322-1329.
4. Nakhushev A. M. On Theory of Boundary Value Problems for Loaded
Integral Equations. Doklady Adygskoy (Cherkesskoy) Mezhdunarodnoy
akademii nauk [Reports Adyghe (Circassian) International Academy of
Sciences], 2014, vol. 16, no. 3, pp. 30-34 [in Russian].
5. Khubiev K. U. On Extremum Principle for Loaded Equations. Doklady
Adygskoy (Cherkesskoy) Mezhdunarodnoy akademii nauk [Reports Adyghe
(Circassian) International Academy of Sciences], 2014, vol. 16, no.
3, pp. 47-50 [in Russian].
6. Nakhushev A. M. Uravneniya matematicheskoy biologii [Equations of
Mathematical Biology]. Moscow, Vysshaya shkola, 1995. 301 p.
7. Khubiev K. U. On Maximum Principle for Characteristicly Loaded
Hyperbolic Type Equation. Materialy 3 Mezhdunarodnogo
Rossiysko-Kazakhskogo simpoziuma "Uravneniya smeshannogo tipa i
rodstvennye problemy analiza i informatiki" [Proc. 3rd Int.
Russian-Kazakh Symp. "Mixed Type Equations and Related Problems of
Analysis and Informatics"]. Nalchik-Terskol, 2014, pp. 219-221 [in
Russian].
8. Dzhuraev T. D., Sopuev A. S., Mamazhanov M. Kraevye zadachi dlya
uravneniy parabolo-giperbolicheskogo tipa [Boundary Value Problems
for Parabolic-Hyperbolic Type Equations]. Tashkent, FAN, 1986. 220p.
9. Agmon S., Nirenberg L., Protter M. A Maximum Principle for a Class
of Hyperbolic Equations and Applications to Equations of Mixed
Elliptic-Hyperbolic Type. Communications on Pure and Applied
Mathematics, 1953, vol. 6, p. 455-470.
