A higher-order Boussinesq equation in locally non-linear theory of one-dimensional non-local elasticity

DOI10.1093/imamat/hxn020zbMath1156.35458OpenAlexW2107828767MaRDI QIDQ3613636

H. A. Erbay, Albert Kohen Erkip, Nilay Duruk Mutlubas

Publication date: 12 March 2009

Published in: IMA Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/c7fe1bf22c7f85901293f512a3aac375ee2e36d2

zbMATH Keywords

Cauchy problemglobal well-posednessnon-local elasticityhigher-order Boussinesq equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Nonlinear elasticity (74B20)

Related Items (12)

Derivation of the Camassa-Holm equations for elastic waves ⋮ The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations ⋮ A dispersive model for undular bores ⋮ Higher order dispersive effects in regularized Boussinesq equation ⋮ Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations ⋮ Numerical solution for a general class of nonlocal nonlinear wave equations arising in elasticity ⋮ Travelling wave solutions to the Benney-Luke and the higher-order improved Boussinesq equations of Sobolev type ⋮ Existence and uniqueness of solutions to initial boundary value problem for the higher order Boussinesq equation ⋮ Exact controllability for nonlocal and nonlinear hyperbolic PDEs ⋮ On the decoupling of the improved Boussinesq equation into two uncoupled Camassa-Holm equations ⋮ Existence and asymptotic behavior of solution of Cauchy problem for the damped sixth-order Boussinesq equation ⋮ On the Cauchy problem for the fractional Camassa-Holm equation

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