Analysis of behavior of solutions’ support for nonlinear partial equations

Authors

  • Kateryna Stiepanova Simon Kuznets Kharkiv National University of Economics Nauky ave., 9-а, Kharkiv, Ukraine, 61166, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2016.80788

Keywords:

solution, Cauchy problem, partial differential equations, support

Abstract

An actual problem is the study of thermal processes in a fairly large range of temperature changes. This, in turn, leads to the study of nonlinear heat equations. In addition, note that in the study of the heat distribution process in space (when we are dealing with a non-constant temperature), as is well known, there are heat flows which are directed from places with higher temperature to places with the lowest temperature. As a result, the equation contains absorption. An adequate mathematical model in this case is a semilinear second-order parabolic equation, which includes the absorption. For such equations, it is very difficult (often impossible) to write the solution explicitly. Therefore, the study of the properties of solutions is an important and urgent problem. The paper analyzes the behavior of the solutions’ support of the Cauchy problem for the above-mentioned above partial differential equation. The result of the research is a theorem, which was proved in the work. It states that under certain conditions on the parameters of the problem, shrinking property of support holds. 

Author Biography

Kateryna Stiepanova, Simon Kuznets Kharkiv National University of Economics Nauky ave., 9-а, Kharkiv, Ukraine, 61166

PhD, Lecturer

Department of Higher Mathematics, Economic and Mathematical Methods

References

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Published

2016-10-30

How to Cite

Stiepanova, K. (2016). Analysis of behavior of solutions’ support for nonlinear partial equations. Eastern-European Journal of Enterprise Technologies, 5(4 (83), 35–40. https://doi.org/10.15587/1729-4061.2016.80788

Issue

Vol. 5 No. 4 (83) (2016): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2016 Kateryna Stiepanova

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