Zdzislav Kamont
abstract:
The following problems for partial functional differential equations are considered:
the Cauchy problem on the Haar pyramid for first order equations, mixed problems
on bounded domains for Hamilton-Jacobi equations, initial boundary value problem of
the Dirichlet tyoe for nonlinear parabolic equations. Impulses depend on functional
variable and they are given at fixed points.
The theory of functional differential inequalities is presented in the paper.
Moreover, discrete versions of theorems on differential inequalities are
presented. The numerical method of lines and difference methods are examples
of applications of the theory.
Mathematics Subject Classification: 35R10.
Key words and phrases: Functional differential inequalities, nonlinear estimates of the Perron type, equations with impulses, comparison theorems, numerical method of lines, stability of difference methods.