On the existence of viscosity solutions for the parabolic differential-functional Cauchy problem
This paper developed solution for nonlinear Cauchy problem for second order differential-functional equations of parabolic type, and provided existence theorems for the class of bounded and in the class of unbounded viscosity solutions. These are based on differential inequalities and on the contraction method. The functional dependence in the equation is of Hale type. The results cover equations with retarded and deviated argument, and differential-integral problems. It is an interesting mathematical paper, the only drawback is that it does not support any formal experiments.
scientific article; zbMATH DE number 5857797