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This result will allow mathematicians to obtain restrictions on the solutions of equations that describe some physical processes, such as diffusion processes and convection processes. The paper is published in the journal Asymptotic Analysis.
Interest in differential inequalities arises from a large number of mathematical modeling problems in natural science, as well as in solving technical and physical problems. It is often necessary to define several functions related to several differential inequalities. It is necessary to have the same number of inequalities to do this. If each of these inequalities is differential, that is, has the form of a relation connecting unknown functions and their derivatives, this is a system of differential inequalities. Systems of differential inequalities describe real physical processes with a certain degree of accuracy (for example, devices that record physical phenomena are not perfect and have some errors). It may turn out that a small error in the initial data causes significant changes in the solution of the inequality. Therefore, it is important to set limits on the solutions of differential equations.
Andrey Shishkov from S.M. Nikol'skii Mathematical Institute of RUDN University and Andrej Kon'kov from Moscow State University obtained the result, which generalizes the classical Keller-Osserman condition for differential equations...
The questions were previously studied mainly for second-order differential operators, and the case of higher-order operators is much less studied. Mathematicians researched higher-order differential inequalities and obtained sufficient stabilization conditions for so-called weak solutions of differential inequalities.
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Additional resources
Andrej Kon'kov et al. On stabilization of solutions of higher order evolution inequalities, Asymptotic Analysis (2019).
DOI: 10.3233/ASY-191522
Source: Phys.Org
