2020/04/22 by Roman Cherniha, Cherniha, Roman, Mykola Serov +3
Mathematics · Medicine · Physics and Astronomy · #35B06 #35Cxx #35K57 #35K58 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2004.10434
openalex publication_date 2020/04/22 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
A class of nonlinear reaction-diffusion-convection equations describing\nvarious processes in physics, biology, chemistry etc. is under study in the\ncase of time and two space variables. The group of equivalence transformations\nis constructed, which is applied for deriving a Lie symmetry classification for\nthe class of such equations by the well-known algorithm.\n It is proved that the algorithm leads to 32 reaction-diffusion-convection\nequations admitting nontrivial Lie symmetries. Furthermore a set of\nform-preserving transformations for this class is constructed in order to\nreduce this number of the equations and obtain a complete Lie symmetry\nclassification. As a result, the so called canonical list of all inequivalent\nequations admitting nontrivial Lie symmetry (up to any point transformations)\nand their Lie symmetries are derived. The list consists of 22 equations and it\nis shown that any other reaction-diffusion-convection equation admitting a\nnontrivial Lie symmetry is reducible to one of these 22 equations. As a\nnontrivial example, the symmetries derived are applied for the reduction and\nfinding exact solutions in the case of the porous-Fisher type equation with the\nBurgers term.\n