Strong nonlinear functional-differential variational inequalities: problems without initial conditions - Bokalo, Mykola; Skira, Iryna; Bokalo, Taras (Frontiers in Applied Mathematics and Statistics, 2024)
Problem without initial conditions for evolution equations and variational inequalities appears in modeling of different nonstationary processes within many fields of science such as ecology, economics, physics, cybernetics, etc, if this processes started a long time ago and initial conditions do not affect on them in the actual time moment. Thus, we can assume that the initial time is minus infinity. In case linear and weakly nonlinear evolution equations and variational inequalities standard initial conditions should be replaced with the behavior of the solution as time variable goes to minus infinity. But for some strongly nonlinear evolution equations and variational inequalities this problem has a unique solution in the class of functions without behavior restriction as time variable goes to minus infinity. In this work, the correctness of the problem without initial conditions for of such type of variational inequalities from a new class, or more precisely, for subdifferential inclusions with functionals, is investigated. Also the estimates of solutions are obtained. The results are new and mostly theoretical in nature.