Geodesic
On the second boundary value problem for nonstationary third-order equations of mixed type
Matematičeskie zametki SVFU, Tome 24 (2017), pp. 76-86.

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We consider the second boundary value problem for nonstationary third-order equations of mixed type. and study asymptotic characteristics of fundamental solutions of the equations, which are used for constructing of regular solutions to the boundary value problems.
Keywords: third order equation, nonstationary pde, uniqueness of solution, regular solution, boundary value problem, mixed type equation, method of potentials, fundamental solution. 
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A. R. Khashimov. On the second boundary value problem for nonstationary third-order equations of mixed type. Matematičeskie zametki SVFU, Tome 24 (2017), pp. 76-86. http://geodesic.mathdoc.fr/item/SVFU_2017_24_a6/

[1] Cattabriga L., “Potenzialli di linea e di dominio per equazioni non paraboliche in due variabili a caratteristiche multiple”, Rend. Sem. Mat. Univ. Padova, 31 (1961), 1–45 | MR | Zbl

[2] Popov S. P., “Numerical simulation of two-soliton solutions to the Zakharov–Kuznetsov equation”, Comput. Math. Math. Phys., 39:10 (1999), 1749–1757 | MR | Zbl

[3] Faminskij A. V., “The Cauchy problem for the Zakharov–Kuznetsov equation”, Differ. Equations, 31:6 (1995), 1070–1081 | MR

[4] Kozhanov A. I., Boundary Value Problems for Mathematical Physics Equations of Odd Order, NSU, Novosibirsk, 1990 | MR

[5] Khashimov A. R., Matnazarov Zh. Sh., “On some properties of fundamental solutions of a non-stationary third-order equation of composite type”, Uzb. Mat. Zh., 2011, no. 1, 170–179

[6] Khashimov A. R., Yakubov S., “On some properties of solutions of the Cauchy problem for a non-stationary third-order equation of composite type”, Ufimsk. Mat. Zh., 6:4 (2014), 139–148

[7] Khashimov A. R., “Some properties of the fundamental solutions of nonstationary third order composite type equation in multidimensional domains”, J. Nonlin. Evol. Equ. Appl., 2013, no. 1, 29–38 | MR

[8] Faminskii A. V., Opritova M. A., “On the Cauchy problem for a Kawahara equation”, Proc. 6th Int. Conf. Differential and Functional-Differential Equations (Moscow, Aug. 14–21, 2011), v. 1, CMFD, 45, Moscow, 2012, 132–150

[9] Katson V. M., “Solitary waves of two-dimensional modified Kawahara equation”, Izv. Vyssh. Uchebn. Zaved., Prikl. Nelinejn. Din., 16:6 (2008), 76–85

[10] Sangare K., Faminskii A. V., “Weak solutions of a mixed problem in a half-strip for a generalized Kawahara equation”, Math. Notes, 85:1 (2009), 98–109 | DOI | MR | Zbl

[11] Faminskii A. V., Kuvshinov R. V., “Initial-boundary value problems for the generalized Kawahara equation”, Russ. Math. Surv., 66:4 (2011), 187–188 | DOI | MR | Zbl

[12] Faminskii A. V., “Nonlocal well-posedness of the mixed problem for the Zakharov–Kuznetsov equation”, J. Math. Sci., 147:1 (2007), 6524–6537, New York | DOI | MR | Zbl

[13] Block H., “Sur les équations linéaires aux dérivées partielles à caractéristiques multiples”, Ark. f. Mat., Astr. och Fys., 7:13, 21 (1912) | Zbl

[14] Del Vecchio E., “La soluzione fondamentale per $\frac{\partial^{3}z}{\partial x^3}-\frac{\partial z}{\partial y}=0$”, Ven. Ist. Atti, 78 (1918-19), 359–382

[15] Del Vecchio E., “Sur deux problèmes d'intégration pour les équations paraboliques”, Ark. för Mat., Astron. och Fys., 11 (1916), 1–13

[16] “Del Vecchio E. Sulle equazioni $\frac{\partial^{3}z}{\partial x^3}-\frac{\partial z}{\partial y}+\phi_1(x,y)=0,$ $\frac{\partial^{3}z}{\partial x^3}-\frac{\partial^2 z}{\partial y^2}+\phi_2(x,y)=0$”, Torino Mem., 66:4 (1915), 1–41 | Zbl

[17] Cattabriga L., “Un problema al. contorno per una equazione parabolica di ordine dispari”, Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat. III. Ser, 13 (1959), 163–203 | MR | Zbl

[18] Abdinazarov S., “On fundamental solutions of linear equations with multiple characteristics of high order”, Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, 1989, no. 4, 3–8 | MR | Zbl

[19] Abdinazarov S., Sobirov Z., “On fundamental solutions of an equation with multiple third-order characteristics in a multidimensional space”, Proc. Int. Sci. Conf. Differential Equations with Partial Derivatives and Related Problems of Analysis and Informatics, Tashkent, 2004, 12–13

[20] Dzhuraev T. D., Abdinazarov S., “On the theory of odd-order equations with multiple characteristics”, Sov. Math., Dokl., 320:6 (1991), 1305–1309 | Zbl

[21] Dzhuraev T. D., Boundary Value Problems for Mixed and Mixed-Composite Type Equations, Fan, Tashkent, 1979 | MR

[22] Kruzhkov S. N., Faminskij A. V., “Generalized solutions of the Cauchy problem for the Korteweg–de Vries equation”, Mat. Sb., N. Ser., 120:3 (1983), 396–425 | MR | Zbl

[23] Eleev V. A., “A boundary value problem for a third-order mixed equation of parabolichyperbolic type”, Ukr. Math. J., 47:1 (1996), 20–29 | MR

[24] Shopolov N. N., “Some boundary-value problems for a parabolic equation of the third order”, C. R. Acad. Bulg. Sci., 1 (1980), 18–21

[25] Roetman E. L., “Some observations about an odd order parabolic equation”, J. Differ. Equ., 9:2 (1971), 335–345 | DOI | MR | Zbl

[26] Khashimov A. R., “On some properties of fundamental solutions of a non-stationary oddorder equation of composite type in multidimensional domains”, Dokl. Akad. Nauk Resp. Uzb., 2010, no. 5, 6–9