We consider a generalized hyperelastic-rod wave equation (or generalized Camassa--Holm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous semigroup of global weak solutions for any initial data from $H^1(\R)$. We also prove a ``weak equals strong''uniqueness result.
Global weak solutions to a generalized hyperelastic-rod wave equation / Coclite, G. M.; Holden, H.; Karlsen, K. H.. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 37:4(2005), pp. 1044-1069. [10.1137/040616711]
Global weak solutions to a generalized hyperelastic-rod wave equation
Coclite, G. M.;
2005-01-01
Abstract
We consider a generalized hyperelastic-rod wave equation (or generalized Camassa--Holm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous semigroup of global weak solutions for any initial data from $H^1(\R)$. We also prove a ``weak equals strong''uniqueness result.File in questo prodotto:
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