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Construction solutions of PDE in parametric form. (English) Zbl 1183.35011


MSC:

35A25 Other special methods applied to PDEs
35C05 Solutions to PDEs in closed form
35G20 Nonlinear higher-order PDEs
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References:

[1] K. A. Volosov, “Gertsenovskie chteniya,” in Proceedings of Gertsen Readings Conference, St. Petersburg, Fla, USA, April 2006.
[2] K. A. Volosov, “Construction of solutions of quasilinear parabolic equations in parametric form,” Differential Equations, vol. 43, no. 4, pp. 507-512, 2007. · Zbl 1131.35313 · doi:10.1134/S001226610704009X
[3] K. A. Volosov, , Doctoral dissertation, MIEM, Moscow, Russia, 2007, http://eqworld.ipmnet.ru.
[4] K. A. Volosov, “Formulas for the exact solutions of quasilinear partial differential equations in implicit form,” Rossiĭskaya Akademiya Nauk. Doklady Akademii Nauk, vol. 418, no. 1, pp. 11-14, 2008. · Zbl 1157.35331 · doi:10.1134/S106456240801002X
[5] Ya. B. Zeldovich, G. I. Barenblatt, V. B. Librovich, and G. M. Makhviladze, Mathematical Theory of Combustion and Explosion, Nauka, Moscow, Russia, 1980.
[6] V. P. Maslov, V. G. Danilov, and K. A. Volosov, Mathematical Modeling of Heat and Mass Transfer Processes (Evolution of Dissipative Structures), Nauka, Moscow, Russia, 1987. · Zbl 0645.73049
[7] V. G. Danilov, V. P. Maslov, and K. A. Volosov, Mathematical Modelling of Heat and Mass Transfer Processes, vol. 348 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1995. · Zbl 0839.35001
[8] A. N. Kolmogorov, I. G. Petrovskii, and I. S. Piskunov, “A study of the diffusion equation with increase in the quantity of matter, and its application to a biological problem,” Moscow State University Bulletin A, vol. 1, no. 6, pp. 1-25, 1937.
[9] K. A. Volosov, “Construction of solutions of quasilinear parabolic equations in parametric form,” Sibirskii Journal of Industrial/noi Matematiki, vol. 11, no. 2(34), pp. 29-39, 2008, English translation in Journal of Applied and Industrial Mathematics. · Zbl 1224.35050
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