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ORIGINAL RESEARCH article

Front. Appl. Math. Stat.
Sec. Dynamical Systems
Volume 10 - 2024 | doi: 10.3389/fams.2024.1467426
This article is part of the Research Topic Approximation Methods and Analytical Modeling Using Partial Differential Equations View all 15 articles

Problem without initial conditions for strongly nonlinear functional-differential variational inequalities

Provisionally accepted
Mykola Bokalo Mykola Bokalo *Iryna Skira Iryna Skira Taras Bokalo Taras Bokalo
  • Department of Mathematical Statistics and Differential Equations, Ivan Franko National University of Lviv, Lviv, Ukraine

The final, formatted version of the article will be published soon.

    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.

    Keywords: parabolic variational inequality, Evolution variational inequality, Evolution inclusion, Subdifferential inclusion, Fourier problem, problem without initial conditions

    Received: 19 Jul 2024; Accepted: 12 Aug 2024.

    Copyright: © 2024 Bokalo, Skira and Bokalo. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Mykola Bokalo, Department of Mathematical Statistics and Differential Equations, Ivan Franko National University of Lviv, Lviv, Ukraine

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