Blow-up of the solution to the initial-value problem in nonlinear three-dimensional hyperelasticity

• Autorzy: J. A. Gawinecki , P. Kacprzyk
• Języki publikacji: EN

Abstrakty

EN

We consider the initial value problem for the nonlinear partial differential equations describing the motion of an inhomogeneous and anisotropic hyperelastic medium. We assume that the stored energy function of the hyperelastic material is a function of the point x and the nonlinear Green-St. Venant strain tensor $e_{jk}$. Moreover, we assume that the stored energy function is $C^∞$ with respect to x and $e_{jk}$. In our description we assume that Piola-Kirchhoff's stress tensor $p_{jk}$ depends on the tensor $e_{jk}$. This means that we consider the so-called physically nonlinear hyperelasticity theory. We prove (local in time) existence and uniqueness of a smooth solution to this initial value problem. Under the assumption about the stored energy function of the hyperelastic material, we prove the blow-up of the solution in finite time.

Kategorie tematyczne

• 35L60: Nonlinear first-order hyperbolic equations
• 35L15: Initial value problems for second-order hyperbolic equations
• 35L55: Higher-order hyperbolic systems
• 35L45: Initial value problems for first-order hyperbolic systems
• 35L35: Initial-boundary value problems for higher-order hyperbolic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2008
• Tom: 35
• Numer: 2
• Strony: 193-208

Daty

wydano

2008

Twórcy

autor

J. A. Gawinecki

• Institute of Mathematics and Cryptology, Faculty of Cybernetics, Military University of Technology, Kaliskiego 2, 00-908 Warszawa 49, Poland

autor

P. Kacprzyk

• Institute of Mathematics and Cryptology, Faculty of Cybernetics, Military University of Technology, Kaliskiego 2, 00-908 Warszawa 49, Poland

Identyfikatory

DOI

10.4064/am35-2-5