Generalized Cauchy problem for hyperbolic functional differential systems
It is considered the following system \[ \partial_tz_i(t,x)=f_i(t,x,z_{\psi(t,x)},\partial_xz_i(t,x)), \quad i=1,\dots,k, \] with the initial condition \[ z_i(t,x)=\varphi_i(t,x) \quad\text{on}\quad E_{0.i}, \] where \(E_{0.i}=[-d_0,a_i]\times\mathbb R^n\). The existence of a weak solution of the system is proved by using a method of successive approximation. The theory of bicharacteristics and integral inequalities is applied. The existence results can be applied to differential systems with deviated arguments and differential integral problems.
scientific article; zbMATH DE number 5858886
scientific article