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 4 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 × Cite Format Result Cite Review PDF 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. · Zbl 0991.35500 [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. · Zbl 0607.35002 [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 · doi:10.1002/cpa.3160060402 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.