Open AccessPosted Content
Nonresonance and global existence of prestressed nonlinear elastic waves
Reads0
Chats0
TLDR
In this article, the nonlinear hyperbolic system of pde's governing the evolution of the deformation of isotropic hyperelastic materials is considered, and the system has global smooth solutions starting close to a one-parameter family of homogeneous dilations.Abstract:
The nonlinear hyperbolic system of pde's governing the evolution of the deformation of isotropic hyperelastic materials is considered. In the absence of boundaries and with an additional nonresonance or null condition, the system has global smooth solutions starting close to a one-parameter family of homogeneous dilations. The proof combines energy estimates with new decay estimates for the linear problem.read more
Citations
More filters
Journal ArticleDOI
Global Solutions for Incompressible Viscoelastic Fluids
TL;DR: In this paper, the existence of both local and global smooth solutions to the Cauchy problem in the whole space and the periodic problem in n-dimensional torus for the incompressible viscoelastic system of Oldroyd-B type in the case of near-equilibrium initial data was proved.
Journal ArticleDOI
Global existence of classical solutions for the two-dimensional oldroyd model via the incompressible limit
TL;DR: The Oldroyd model describing fluids with viscoelastic properties with small initial displacements with main difficulty is the lack of the damping mechanism on the deformation tensor.
Journal ArticleDOI
Long-time existence of quasilinear wave equations exterior to star-shaped obstacles via energy methods
TL;DR: It is established long-time existence results for quasilinear wave equations in the exterior of star-shaped obstacles by proving an analogue of the mixed-norm estimates of Keel, Smith, and Sogge for the perturbed wave equation.
Journal ArticleDOI
Global existence for three-dimensional incompressible isotropic elastodynamics via the incompressible limit
Thomas C. Sideris,Becca Thomases +1 more
TL;DR: The existence of global-in-time classical solutions to the Cauchy problem for incompressible nonlinear isotropic elastodynamics for small initial displacements is proved in this paper.
Posted Content
Almost global existence for some semilinear wave equations
TL;DR: In this article, the authors proved almost global existence for semilinear wave equations outside of nontrapping obstacles using the vector field method, but only use the generators of translations and Euclidean rotations.
References
More filters
Book
Non-Linear Elastic Deformations
TL;DR: In this paper, the influence of non-linear elastic systems on a simple geometric model for elastic deformations is discussed, and the authors propose a planar and spatial euler introduction to nonlinear analysis.
Journal ArticleDOI
Uniform decay estimates and the lorentz invariance of the classical wave equation
TL;DR: In this paper, le comportement asymptotique des solutions de □u=0 ou □=∂ t 2 −∂ 1 2...−∂ n 2 pour des conditions initiales u=0, u t =g(x) en t=0.
Journal ArticleDOI
Global solutions of nonlinear hyperbolic equations for small initial data
TL;DR: In this paper, a systemes quasilineaires d'equations hyperboliques d'ordre 2 qui sont des deformations non lineaires de l'equation d'onde.
Journal ArticleDOI
Blow-Up for Quasi-Linear Wave Equations in Three Space Dimensions,
TL;DR: In this article, the authors consider equations of the form ============\/\/\/\/\/\/£££ £ £££€££/$££$£ £€£ ££ £/$£ £$££