Add to ORKGWe are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we develop such connections for the case of two spatial dimensions, and demonstrate that the continuum mechanical equations can be mapped into a corresponding geometric framework and the inherent direct application of the theory of isometric embeddings and the Gauss–Codazzi equations through examples for the Euler equations for fluids and the Euler–Lagrange equations for elastic solids. These results show that the geometric theory provides an avenue for addressing the admissibility criteria for nonlinear conserv...
In this thesis we consider systems of partial differential equations of continuum mechanics and anal...
In fluid mechanics, the vorticity provides a valuable alternative perspective of the behavior of flo...
The linear elastostatics complex can be used to find stable numerical schemes. In this paper, we sho...
We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riem...
In the thesis we investigate two problems on Partial Differential Equations (PDEs) in differential geo...
The isometric embedding problem is a fundamental problem in differential geometry. A longstanding pr...
We investigate the systems of quasi-linear partial differential equations of hydrody- namic type. Th...
We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose...
This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized contin...
Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions...
In this PhD thesis, we propose a theoretical framework for studying referential and spatial evolutio...
We study trapped surfaces from the point of view of local isometric embedding into 3D Riemannian ma...
We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the ...
This paper concerns the elastic structures which exhibit non-zero strain at free equilibria. Many gr...
Elasticity is the prototype of constitutive models in Continuum Mechanics. In the nonlinear range, t...
In this thesis we consider systems of partial differential equations of continuum mechanics and anal...
In fluid mechanics, the vorticity provides a valuable alternative perspective of the behavior of flo...
The linear elastostatics complex can be used to find stable numerical schemes. In this paper, we sho...
We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riem...
In the thesis we investigate two problems on Partial Differential Equations (PDEs) in differential geo...
The isometric embedding problem is a fundamental problem in differential geometry. A longstanding pr...
We investigate the systems of quasi-linear partial differential equations of hydrody- namic type. Th...
We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose...
This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized contin...
Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions...
In this PhD thesis, we propose a theoretical framework for studying referential and spatial evolutio...
We study trapped surfaces from the point of view of local isometric embedding into 3D Riemannian ma...
We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the ...
This paper concerns the elastic structures which exhibit non-zero strain at free equilibria. Many gr...
Elasticity is the prototype of constitutive models in Continuum Mechanics. In the nonlinear range, t...
In this thesis we consider systems of partial differential equations of continuum mechanics and anal...
In fluid mechanics, the vorticity provides a valuable alternative perspective of the behavior of flo...
The linear elastostatics complex can be used to find stable numerical schemes. In this paper, we sho...