Hyperbolic functional-differential equations with unbounded delay
The author studies the existence and uniqueness of Carathéodory solutions for quasilinear equations with unbounded delay \[ D_t z(t,x) +\sum^n_{i=1} \rho_i (t,x,z_{(t,x)}) D_{x_i} z(t,x)= f(t,x,z_{(t,x)}), \] \[ z(t,x)= \varphi(t,x) \quad\text{on} \quad (-\infty,0] \times \mathbb{R}^n, \] where \(z_{(t,x)} (\tau,s)= z(t+ \tau,x+s)\), \((\tau,s)\in D\). To this end, the method of bicharacteristics and the method of integral inequalities are used.
scientific article; zbMATH DE number 1278888
scientific article