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

J. A. Gawinecki, and P. Kacprzyk. "Blow-up of the solution to the initial-value problem in nonlinear three-dimensional hyperelasticity." Applicationes Mathematicae 35.2 (2008): 193-208. <http://eudml.org/doc/280062>.

@article{J2008,
abstract = {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.},
author = {J. A. Gawinecki, P. Kacprzyk},
journal = {Applicationes Mathematicae},
keywords = {local existence and uniqueness; physically nonlinear hyperelasticity},
language = {eng},
number = {2},
pages = {193-208},
title = {Blow-up of the solution to the initial-value problem in nonlinear three-dimensional hyperelasticity},
url = {http://eudml.org/doc/280062},
volume = {35},
year = {2008},
}

TY - JOUR
AU - J. A. Gawinecki
AU - P. Kacprzyk
TI - Blow-up of the solution to the initial-value problem in nonlinear three-dimensional hyperelasticity
JO - Applicationes Mathematicae
PY - 2008
VL - 35
IS - 2
SP - 193
EP - 208
AB - 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.
LA - eng
KW - local existence and uniqueness; physically nonlinear hyperelasticity
UR - http://eudml.org/doc/280062
ER -