M. I. Besova, V. I. Kachalov, “On a nonlinear differential equation in a Banach space”, Sib. Èlektron. Mat. Izv., 2021, Volume 18, Issue 1,Pages <nobr>332

This article is cited in 2 papers

Differentical equations, dynamical systems and optimal control

On a nonlinear differential equation in a Banach space

M. I. Besova, V. I. Kachalov

National Research University «MPEI», 14, Krasnokazarmennaya str., Moscow, 111250, Russia

Abstract: An Navier-Stokes type equation is considered for which a generalized solution is constructed in the form of a series in powers of a specially introduced parameter and its convergence is proved. An example of a mixed problem for the Burgers equation is given.

Keywords: equations of Navier-Stokes type, Burgers equation, generalized solution, holomorphic dependence of a solution on a parameter.

UDC: 517.956.8

MSC: 35L05, 35K03, 35J05, 35J10

Received February 17, 2020, published March 30, 2021

DOI: 10.33048/semi.2021.18.022