TY - JOUR
AU - S. P. Lavrenyuk
AU - P. Ya. Pukach
PY - 2007/11/25
Y2 - 2023/03/31
TI - Mixed problem for a nonlinear hyperbolic equation in a domain unbounded with respect to space variables
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 59
IS - 11
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3408
AB - We investigate the first mixed problem for a quasilinear hyperbolic equation of the second order with power nonlinearity in a domain unbounded with respect to space variables. We consider the case of an arbitrary number of space variables. We obtain conditions for the existence and uniqueness of the solution of this problem independent of the behavior of solution as $|x| \rightarrow +\infty$. The indicated classes of the existence and uniqueness are defined as spaces of local integrable functions. The dimension of the domain in no way limits the order of nonlinearity.
ER -