Geodesic
Superposition principle and exact solutions of a nonlinear diffusion
Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 1, pp. 36-50

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We present a method for constructing exact solutions of nonlinear diffusion equations in a one-dimensional coordinate space using a special superposition principle. As equations of nonlinear diffusion, we take equations of the form $n_t-(\ln n)_{xx}+\mu n+\gamma n^2-g=0$, which play an important role in the problem of the emergence of regular structures in nonlinear media under the action of external radiation sources. The method is based on using differential properties of polynomials in functional parameters. We present concrete solutions and analyze some of their common properties.
Keywords: nonlinear diffusion equation, regular structure.
Mots-clés : exact solution, superposition principle 
V. M. Zhuravlev. Superposition principle and exact solutions of a nonlinear diffusion. Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 1, pp. 36-50. http://geodesic.mathdoc.fr/item/TMF_2015_183_1_a1/
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[1] A. A. Samarskii, A. P. Mikhailov, Matematicheskoe modelirovanie. Idei. Metody. Primery, Nauka, M., 1997 | MR | MR | Zbl | Zbl

[2] A. A. Samarskii, V. A. Galaktionov, S. P. Kurdyumov, A. P. Mikhailov, Rezhimy s obostreniem v zadachakh dlya kvazilineinykh parabolicheskikh uravnenii, Nauka, M., 1987 | DOI | MR | MR | Zbl

[3] V. V. Pukhnachev, Prikl. mekhanika i tekhn. fizika, 36:2 (1995), 23–31 | MR | Zbl

[4] S. N. Aristov, Prikl. mekhanika i tekhn. fizika, 40:1 (1999), 22–26 | MR | Zbl

[5] V. M. Zhuravlev, TMF, 124:2 (2000), 265–278 | DOI | DOI | MR | Zbl

[6] V. M. Zhuravlev, Pisma v ZhETF, 75:1 (2002), 11–16 | DOI

[7] V. M. Zhuravlev, ZhETF, 129:3 (2006), 587–604 | DOI