Geodesic
Non-autonomous evolutionary equation of Monge--Ampere type with two space variables
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2023), pp. 66-80

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There are investigated the exact solutions of non-autonomous evolutionary equation with two space variables, the right side of which contains Monge–Ampere operator. The solutions with additive and multiplicative separation of variables are founded. There are considered the reductions of the given equation to ordinary differential equations (ODE). The classic and generalized self-similar solutions, and the solutions with functional separation of variables are received. In particular, it is shown that the given equation can be reduced to ODE, if the coefficient at the time derivative can be represented in the form of production of the functions depend on time, space variables, and unknown function. Also the reductions of the given equation to two-dimensional PDE are founded.
Keywords: evolutionary equation, Monge–Ampere equation, reduction, separation of variables, self-similar solution. 
@article{IVM_2023_2_a5,
     author = {I. V. Rakhmelevich},
     title = {Non-autonomous evolutionary equation of {Monge--Ampere} type with two space variables},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {66--80},
     publisher = {mathdoc},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_2_a5/}
}
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I. V. Rakhmelevich. Non-autonomous evolutionary equation of Monge--Ampere type with two space variables. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2023), pp. 66-80. http://geodesic.mathdoc.fr/item/IVM_2023_2_a5/