caa a22 4500 47574215X CHVBK 20180406123502.0 cr unu---uuuuu 170329e20000201xx s 000 0 eng 10.1007/BF02686247 doi (NATIONALLICENCE)springer-10.1007/BF02686247 Non-self-similar solutions of multidimensional nonlinear diffusion equations [Elektronische Daten] [G. Rudykh, É. Semenov] An original construction of the exact nonnegative solution of multidimensional nonlinear diffusion equations is proposed and studied. On substituting this construction into the original equation, we obtain a system of algebro-differential equations in which the number of equations exceeds the number of unknown functions. It is proved that the resulting system possesses nontrivial solutions. On the basis of this result, we construct exact non-self-similar explicit nonnegative solutions anisotropic with respect to the space variables both of the class of equations of a porous medium (nonstationary filtration) and of the class of equations involving nonlinear thermal conductivity with negative exponent. In particular, this class contains the so-called equations of rapid and limit diffusion. Kluwer Academic/Plenum Publishers, 2000 non-self-similar solution nationallicence multidimensional nonlinear diffusion equation nationallicence system of algebro-differential equations nationallicence nonstationary filtration nationallicence nonlinear thermal conductivity nationallicence rapid diffusion nationallicence limit diffusion nationallicence Rudykh G. Institute of System Dynamics and Control Theory, Siberian Division of the Russian Academy of Sciences, USSR aut Semenov É. Institute of System Dynamics and Control Theory, Siberian Division of the Russian Academy of Sciences, USSR aut Mathematical Notes Springer US 67/2(2000-02-01), 200-206 0001-4346 67:2<200 2000 67 11006 https://doi.org/10.1007/BF02686247 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02686247 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Rudykh G. Institute of System Dynamics and Control Theory, Siberian Division of the Russian Academy of Sciences, USSR aut NATIONALLICENCE 700 1- Semenov É. Institute of System Dynamics and Control Theory, Siberian Division of the Russian Academy of Sciences, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Springer US 67/2(2000-02-01), 200-206 0001-4346 67:2<200 2000 67 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer