Abstract:
Some exact solutions to a nonlinear heat equation are constructed. An initial-boundary value problem is examined for a nonlinear heat equation. To construct solutions, the problem for a partial differential equation of the second order is reduced to a similar problem for a first order partial differential equation.
Keywords:
nonlinear partial differential equations, heat equation, boundary value problem, initialboundary value problem.
Citation:
L. I. Rubina, O. N. Ul'yanov, “On some method for solving a nonlinear heat equation”, Sibirsk. Mat. Zh., 53:5 (2012), 1091–1101; Siberian Math. J., 53:5 (2012), 872–881
This publication is cited in the following 14 articles:
Alexander Kazakov, Anna Lempert, “Multidimensional Diffusion-Wave-Type Solutions to the Second-Order Evolutionary Equation”, Mathematics, 12:2 (2024), 354
S. A. Zinina, A. I. Popov, A. V. Eremin, “Chislennoe reshenie nelineinoi zadachi teploprovodnosti v poristoi plastine s uporyadochennoi makrostrukturoi”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2024, no. 1, 53–67
A. L. Kazakov, “Resheniya c nulevym frontom dlya kvazilineinogo parabolicheskogo uravneniya teploprovodnosti”, Tr. IMM UrO RAN, 30, no. 2, 2024, 86–102
S. P. Bautin, I. A. Vazieva, “PREDSTAVLENIE REShENII ODNOMERNOGO NELINEINOGO URAVNENIYa TEPLOPROVODNOSTI TRIGONOMETRIChESKIMI RYaDAMI”, Vestnik, 13:3 (2024), 154
A. L. Kazakov, P. A. Kuznetsov, L. F. Spevak, “The Problem of Diffusion Wave Initiation for a Nonlinear Second-Order Parabolic System”, Proc. Steklov Inst. Math. (Suppl.), 321, suppl. 1 (2023), S109–S126
L. I. Rubina, “Ob odnom podkhode k resheniyu volnovogo uravneniya dlya dielektricheskikh nemagnitnykh sred”, Tr. IMM UrO RAN, 29, no. 2, 2023, 145–156
A. L. Kazakov, A. A. Lempert, “Tochnye resheniya tipa diffuzionnykh voln dlya nelineinogo vyrozhdayuschegosya parabolicheskogo uravneniya vtorogo poryadka”, Tr. IMM UrO RAN, 28, no. 3, 2022, 114–128
L. I. Rubina, O. N. Ulyanov, “On double wave type flows”, Siberian Math. J., 60:4 (2019), 673–684
A. L. Kazakov, P. A. Kuznetsov, “On the analytic solutions of a special boundary value problem for a nonlinear heat equation in polar coordinates”, J. Appl. Industr. Math., 12:2 (2018), 255–263
L. I. Rubina, O. N. Ul'yanov, “On the problem of the flow of an ideal gas around bodies”, Proc. Steklov Inst. Math. (Suppl.), 301, suppl. 1 (2018), 145–154
L. I. Rubina, O. N. Ulyanov, “Ob odnom podkhode k resheniyu neodnorodnykh uravnenii v chastnykh proizvodnykh”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:3 (2017), 355–364
L. I. Rubina, O. N. Ulyanov, “Dva podkhoda k resheniyu uravneniya potentsiala v avtomodelnykh peremennykh”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:3 (2015), 30–38
A. I. Korotkii, N. A. Artemova, N. A. Vaganova, O. O. Kovrizhnykh, L. I. Rubina, O. N. Ulyanov, O. V. Ushakova, M. Yu. Filimonov, I. A. Tsepelev, “O razrabotkakh analiticheskikh i chislennykh metodov resheniya zadach mekhaniki sploshnoi sredy”, Tr. IMM UrO RAN, 19, no. 2, 2013, 203–215