Odd-order quasilinear evolution equations posed on a bounded interval - 10.5269/bspm.v28i1.10816

Abstract

We study in a rectangle Q_T = (0, T)×(0, 1) global well-posedness of nonhomo-geneous initial-boundary value problems for general odd-order quasilinear partial differential equations. This class of equations includes well-known Korteweg–de Vries and Kawahara equations which model the dynamics of long small-amplitude waves in various media. Our study is motivated by physics and numerics and our main goal is to formulate a correct nonhomogeneous initial-boundary value problem under consideration in a bounded interval and to prove the existence and uniqueness of global in time weak and regular solutions in a large scale of Sobolev spaces as well as to study decay of solutions while t → ∞.