Non-uniform dependence and well-posedness for the hyperelastic rod equation

DOI10.1016/j.jde.2010.04.002zbMath1193.35221OpenAlexW1996844149MaRDI QIDQ983270

David Karapetyan

Publication date: 22 July 2010

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2010.04.002

zbMATH Keywords

Sobolev spacesenergy estimatesapproximate solutionswell-posednessinitial value problemperiodichyperelastic rod equationnon-periodicnon-uniform dependencecontinuity of solution map

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Smoothness and regularity of solutions to PDEs (35B65) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (15)

Non‐uniform dependence on initial data of a modified periodic two‐component Camassa‐Holm system ⋮ Non-uniform dependence on initial data for the modified \(\mu\)-Camassa-Holm equation ⋮ Non-uniform continuity of the semiflow map associated to the porous medium equation ⋮ Non-uniform dependence on initial data for the \({\mu-b}\) equation ⋮ On the well-posedness of the hyperelastic rod equation ⋮ A note on the Cauchy problem for the periodic two-component Novikov system ⋮ Local well-posedness and decay for some generalized shallow water equations ⋮ Non-uniform dependence on initial data for the two-component Novikov system ⋮ Hölder continuity for a modified Camassa-Holm system ⋮ Global attractor for the generalized hyperelastic-rod equation ⋮ Nonuniform dependence and persistence properties for a two-component Novikov system ⋮ Non-uniform continuity of the flow map for an evolution equation modeling shallow water waves of moderate amplitude ⋮ On solitonic solutions for the hyperelastic rod equation ⋮ Non-uniform dependence for a modified Camassa-Holm system ⋮ On well-posedness of two-component Camassa-Holm system in the critical Besov space

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