Odd-Order Quasilinear Evolution Equations with General Nonlinearity on Bounded Intervals

Abstract: An initial-boundary value problem posed on a bounded interval is considered for a class of odd-order (more than one) quasilinear evolution equations with general nonlinearity. Assumptions on the equations do not provide global a priori estimates for solutions of an arbitrary size. For small initial and boundary data, small right-hand side function results on global existence and uniqueness of small weak solutions, as well as on their large-time exponential decay are established. © 2021, Pleiades Publishing, Ltd.