Multiple solutions to elliptic inclusions via critical point theory on closed convex sets
Variational analysis of semilinear plate equation with free boundary conditions
July 2015, 35(7): 3103-3131. doi: 10.3934/dcds.2015.35.3103
Asymptotics in shallow water waves
Robert McOwen 1, and Peter Topalov 1,
Northeastern University, 360 Huntington Avenue, Boston, MA 02115, United States, United States
Received August 2014 Revised September 2014 Published January 2015
In this paper we consider the initial value problem for a family of shallow water equations on the line $\mathbb{R}$ with various asymptotic conditions at infinity. In particular we construct solutions with prescribed asymptotic expansion as $x\to\pm\infty$ and prove their invariance with respect to the solution map.
Keywords: spatial asymptotics, well-posedness of non-linear PDEs, Camassa-Holm equation., Shallow water waves, groups of asymptotic diffeomorphisms.
Mathematics Subject Classification: 35Q35, 37K65, 35Q53, 37K1.
Citation: Robert McOwen, Peter Topalov. Asymptotics in shallow water waves. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 3103-3131. doi: 10.3934/dcds.2015.35.3103
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Robert McOwen Peter Topalov