Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions

2013/09/30 by Soichiro Katayama, Akitaka Matsumura, Hideaki Sunagawa
Mathematics · #math.AP #msc:35L71 #msc:35B40

paper · pdf · doi:10.1007/s00030-014-0297-7

published as Nonlinear Differential Equations and Applications NoDEA, vol.22 (2015) no.4, 601-628 · 28 pages. arXiv admin note: text overlap with arXiv:1206.0066

arxiv created 2014/06/06 · arxiv updated 2015/10/13

Abstract

We consider the Cauchy problem for systems of semilinear wave equations in two space dimensions. We present a structural condition on the nonlinearity under which the energy decreases to zero as time tends to infinity if the Cauchy data are sufficiently small, smooth and compactly-supported.

Citations

• Semilinear hyperbolic systems violating the null condition