Chen, Min; Dumont, Serge; Dupaigne, Louis; Goubet, Olivier Decay of solutions to a water wave model with a nonlocal viscous dispersive term. (English) Zbl 1198.35190 Discrete Contin. Dyn. Syst. 27, No. 4, 1473-1492 (2010). Authors’ abstract: We investigate a water wave model with a nonlocal viscous term \[ u_t + u_x+ \beta u_{xxx}+ \frac {\sqrt{\nu}} {\sqrt{\pi}} \int_0^t \frac {u_t(s)}{\sqrt{t-s}}\,ds + uu_{x} = \nu u_{xx}. \]The wellposedness of the equation and the decay rate of solutions are investigated theoretically and numerically. Reviewer: Nicolae Pop (Baia Mare) Cited in 2 ReviewsCited in 13 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) 74M15 Contact in solid mechanics 76M22 Spectral methods applied to problems in fluid mechanics Keywords:finite element analysis; nonlocal friction; rigid-plastic material; variational formulations; weak solutions PDFBibTeX XMLCite \textit{M. Chen} et al., Discrete Contin. Dyn. Syst. 27, No. 4, 1473--1492 (2010; Zbl 1198.35190) Full Text: DOI