Unique classical solvability of the Rosenau–Burgers equation on the line and the half-line

I. K. Katasheva

Mozhaiskiy Space Military Academy, St. Petersburg

Abstract: We examine the classical local solvability for the Cauchy problem and boundary-value problems on the half-line for the Rosenau–Burgers equation. Using the method of test functions we also obtain an upper bound of the blow-up time.

Keywords: nonlinear equations, blow-up, local solvability, a priori estimate

UDC: 517.957

MSC: 35Bxx

DOI: 10.36535/2782-4438-2025-246-21-34