Uniqueness and continuous dependence on data for one-dimensional impact problems
Schatzman, Michelle
HAL, hal-01544389 / Harvested from HAL
Text on HAL
One dimensional dynamics with impact are described by the data of a closed interval $K$, a function $f$ of time, position, and velocity, and a restitution coefficient $e \in [0,1)$. When $u$ is in the interior of $K$, it satisfies the ordinary differential equation $\ddot{u} =f(t,u,\dot{u})$. When it hits the end points of $K$, the velocity is reversed and multiplied by $e$. If f is analytic with respect to its three arguments, it is proved that uniqueness holds for the forward Cauchy problem.
Publié le : 1998-07-04
Classification:  Uniqueness of the Cauchy problem,  Vibro-impact system,  Continuous dependence,  [MATH]Mathematics [math] 
@article{hal-01544389,
     author = {Schatzman, Michelle},
     title = {Uniqueness and continuous dependence on data for one-dimensional impact problems},
     journal = {HAL},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01544389}
}

Schatzman, Michelle. Uniqueness and continuous dependence on data for one-dimensional impact problems. HAL, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/hal-01544389/