On the Cauchy problem for hyperbolic functional-differential equations
Volume 115 / 2015
Annales Polonici Mathematici 115 (2015), 53-74
MSC: Primary 35A01; Secondary 35L71, 35R10.
DOI: 10.4064/ap115-1-5
Abstract
We consider the Cauchy problem for a nonlocal wave equation in one dimension. We study the existence of solutions by means of bicharacteristics. The existence and uniqueness is obtained in $W^{1,\infty }_{\rm loc}$ topology. The existence theorem is proved in a subset generated by certain continuity conditions for the derivatives.
