Abstract:
The paper considers the stochastic space-fractional Kuramoto – Sivashinsky equation in the
complex plane. This equation is reduced to an ordinary differential equation. For the resulting
ODE, a theorem on the existence and uniqueness of the Cauchy problem in a neighborhood of
the initial data is formulated and proved. For practical applications, an analytical approximate
solution (a partial sum of a series) is proposed. A priori error estimates of the analytical
approximate solution are provided. To extend beyond the domain of convergence of the series
obtained, an analytic continuation of the approximate solution is carried out.
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