4 research outputs found
The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model
This paper studies the Cauchy problem for a one-dimensional nonlinear
peridynamic model describing the dynamic response of an infinitely long elastic
bar. The issues of local well-posedness and smoothness of the solutions are
discussed. The existence of a global solution is proved first in the sublinear
case and then for nonlinearities of degree at most three. The conditions for
finite-time blow-up of solutions are established.Comment: To appear in Journal of Differential Equations (added references,
corrected typos, minor revision in Section 2, 18 pages
The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model
This paper studies the Cauchy problem for a one-dimensional nonlinear
peridynamic model describing the dynamic response of an infinitely long elastic
bar. The issues of local well-posedness and smoothness of the solutions are
discussed. The existence of a global solution is proved first in the sublinear
case and then for nonlinearities of degree at most three. The conditions for
finite-time blow-up of solutions are established.Comment: To appear in Journal of Differential Equations (added references,
corrected typos, minor revision in Section 2, 18 pages