Small Parameter Method in the Theory of Burgers-Type Equations

The Burgers equation, introduced by G. Bateman in 1915 and studied by J.M. Burgers in 1948, has found wide application in fluid mechanics, nonlinear acoustics, and other areas of applied mathematics. Approaches to its solution were very diverse: asymptotic, numerical, and analytical. In this paper, an analytical method for solving a Burgers-type equation in a Banach space is developed. Namely, after artificially introducing a small parameter into the equation, the existence of an analytical solution with respect to this parameter is proved. In this case, a multidimensional version of the Burgers equation is also considered.