Two-dimensional elliptic equation with nonlinear source containing powers of first derivatives

Author(s):  I.V. Rakhmelevich, Dr., associate Professor, Nizhny Novgorod State University, Nizhny Novgorod, Russia,

Issue:  Volume 49, №27

Rubric:  Mathematics

Annotation:  There is investigated two-dimensional non-autonomous elliptic equation, right side of which contains the arbitrary nonlinearity on unknown function and power-law nonlinearities on its first derivatives. There are received the solutions of this equation with additive and multiplicative separation of variables, and also solutions of travelling wave type, self-similar and spherically symmetric solutions. The conditions of existence of founded solutions are formulated. The dependence of solutions on parameters of equation is investigated

Keywords:  partial differential equation, elliptic equation, ordinary differential equation, separation of variables, power-law nonlinearity, solution of travelling wave type, self-similar solution

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