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Information × Registration Number 0223U003993, 0122U201960 , R & D reports Title Extended group analysis of reaction–diffusion equations modeling physical and biological processes popup.stage_title Head Vanieieva Olena O., Доктор фізико-математичних наук Registration Date 04-08-2023 Organization Vanieieva Olena O. popup.description2  The object of research is nonlinear model equations of mathematical physics and biology. The aim of the work is to solve classification problems of group analysis, in particular, the problems of classification of admissible transformations, Lie symmetries and reductions, as well as to construct exact solutions for (1+1)-dimensional nonlinear equations of reaction-diffusion type, Korteweg-de Vries and Kawahara equations. Research methods include improved methods of group analysis of nonlinear differential equations, in particular, the equivalence method, the Lie reduction method, and the method of mapping between classes. Admissible transformations of the class of generalized reaction-diffusion equations with variable coefficients have been studied. For several subclasses, the property of normalization has been investigated, equivalence groups have been constructed, and classifications of conservation laws have been performed. Exhaustive classifications of Lie symmetries for two similar classes of reaction-diffusion equations with variable coefficients dependent on the time variable have also been carried out. As a result of the classification of Lie symmetries, model equations with nontrivial symmetry properties have been identified, which could potentially be more interesting for applications. Exact solutions have been constructed for the class of generalized Korteweg-de Vries and Kawahara equations with variable coefficients. It has been demonstrated that the equivalebce method is more effective than the methods previously applied by other authors. The results of the work are theoretical in nature and can be applied in further research in the group analysis of differential equations, as well as in mathematical physics and biology for studying models of real physical and biological processes. Product Description popup.authors Vanieieva Olena O. popup.nrat_date 2023-08-04 Close