POPOVYCH, Roman, Stanislav OPANASENKO a Vyacheslav BOYKO. Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity. Journal of Mathematical Analysis and Applications. San Diego (USA): Academic Press Inc. Elsevier Science, 2020, roč. 484, č. 1, s. "123739-1"-"123739-30", 30 s. ISSN 0022-247X. Dostupné z: https://dx.doi.org/10.1016/j.jmaa.2019.123739. |
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@article{39681, author = {Popovych, Roman and Opanasenko, Stanislav and Boyko, Vyacheslav}, article_location = {San Diego (USA)}, article_number = {1}, doi = {http://dx.doi.org/10.1016/j.jmaa.2019.123739}, keywords = {Group classification of differential equations; Method of furcate splitting; Diffusion-reaction equations; Lie symmetry; Equivalence group; Lie reduction}, language = {eng}, issn = {0022-247X}, journal = {Journal of Mathematical Analysis and Applications}, title = {Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity}, url = {https://www.sciencedirect.com/science/article/pii/S0022247X19310078?via%3Dihub}, volume = {484}, year = {2020} }
TY - JOUR ID - 39681 AU - Popovych, Roman - Opanasenko, Stanislav - Boyko, Vyacheslav PY - 2020 TI - Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity JF - Journal of Mathematical Analysis and Applications VL - 484 IS - 1 SP - "123739-1"-"123739-30" EP - "123739-1"-"123739-30" PB - Academic Press Inc. Elsevier Science SN - 0022247X KW - Group classification of differential equations KW - Method of furcate splitting KW - Diffusion-reaction equations KW - Lie symmetry KW - Equivalence group KW - Lie reduction UR - https://www.sciencedirect.com/science/article/pii/S0022247X19310078?via%3Dihub L2 - https://www.sciencedirect.com/science/article/pii/S0022247X19310078?via%3Dihub N2 - We carry out the enhanced group classification of a class of (1+1)-dimensional nonlinear diffusion-reaction equations with gradient-dependent diffusivity using the two-step version of the method of furcate splitting. For simultaneously finding the equivalence groups of an unnormalized class of differential equations and a collection of its subclasses, we suggest an optimized version of the direct method. The optimization includes the preliminary study of admissible transformations within the entire class and the successive splitting of the corresponding determining equations with respect to arbitrary elements and their derivatives depending on auxiliary constraints associated with each of required subclasses. In the course of applying the suggested technique to subclasses of the class under consideration, we construct, for the first time, a nontrivial example of finite-dimensional effective generalized equivalence group. Using the method of Lie reduction and the generalized separation of variables, exact solutions of some equations under consideration are found. ER -
POPOVYCH, Roman, Stanislav OPANASENKO a Vyacheslav BOYKO. Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity. \textit{Journal of Mathematical Analysis and Applications}. San Diego (USA): Academic Press Inc. Elsevier Science, 2020, roč.~484, č.~1, s.~''123739-1''-''123739-30'', 30 s. ISSN~0022-247X. Dostupné z: https://dx.doi.org/10.1016/j.jmaa.2019.123739.
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