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Khubiev, Kazbek Uzeirovich

A maximum principle for a loaded hyperbolic-parabolic equation. (Russian. English summary) Zbl 1474.35155

Vladikavkaz. Mat. Zh. 18, No. 4, 80-85 (2016).
Summary: 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.

Cited in 2 Documents

MSC:

35B50 Maximum principles in context of PDEs
35M12 Boundary value problems for PDEs of mixed type

Keywords:

maximum principle; loaded equation; equation of mixed type; hyperbolic-parabolic equation
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\textit{K. U. Khubiev}, Vladikavkaz. Mat. Zh. 18, No. 4, 80--85 (2016; Zbl 1474.35155)
Full Text: MNR

References:

[1] Nakhushev A. M., #Nagruzhennye uravneniya i ikh prilozheniya, Nauka, M., 2012, 232 pp.
[2] Bitsadze A. V., “O nekotorykh zadachakh smeshannogo tipa”, #Dokl. AN SSSR, #70:4 (1950), 561-565
[3] Sabitov K. B., “O printsipe maksimuma dlya uravnenii smeshannogo tipa”, #Differents. uravneniya, #24:11 (1988), 1967-1976 · Zbl 0677.35074
[4] Nakhushev A. M., “K teorii kraevykh zadach dlya nagruzhennykh integralnykh uravnenii”, #Dokl. Adygskoi (Cherkesskoi) Mezhdunar. akademii nauk, #16:3 (2014), 30-34
[5] Khubiev K. U., “O printsipe ekstremuma dlya nagruzhennykh uravnenii”, #Dokl. Adygskoi (Cherkesskoi) Mezhdunar. akademii nauk, #16:3 (2014), 47-50
[6] Nakhushev A. M., #Uravneniya matematicheskoi biologii, Vyssh. shk., M., 1995, 301 pp.
[7] Khubiev K. U., “O printsipe maksimuma dlya kharakteristicheski nagruzhennogo uravneniya giperbolicheskogo tipa”, #Uravneniya smeshannogo tipa i rodstvennye problemy analiza i informatiki, Materialy III Mezhdunar. Rossiisko-Kazakhskogo simp. (Nalchik-Terskol, 3-7 dekabrya 2014 g.), 219-221
[8] Dzhuraev T. D., Sopuev A., Mamazhanov M., #Kraevye zadachi dlya uravnenii parabolo-giperbolicheskogo tipa, Fan, Tashkent, 1986, 220 pp.
[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”, #Commun. Pure Appl. Math., #6 (1953), 455-470 · Zbl 0090.07401
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