On Solving the Cauchy Problem for Parabolic Equation with Nonlocal Potential

Victor G.  Bondarenko

doi:10.1615/JAutomatInfScien.v44.i12.30

Journal of Automation and Information Sciences

Editor-in-Chief: Arkadiy A. Chikriy (open in a new tab)

Associate Editors: Vyacheslav F. Gubarev (open in a new tab) Yuriy P. Kondratenko (open in a new tab) Nonna V. Turovyerova (open in a new tab)

Published 12 issues per year

ISSN Print: 1064-2315

ISSN Online: 2163-9337

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On Solving the Cauchy Problem for Parabolic Equation with Nonlocal Potential

Volume 44, Issue 12, 2012, pp. 23-27

DOI: 10.1615/JAutomatInfScien.v44.i12.30

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Victor G. Bondarenko
National Technical University of Ukraine "Igor Sikorsky Kiev Polytechnic Institute", Kiev

ABSTRACT

We consider parabolic equation in n-dimensional space with nonlocal nonlinear potential of convolution type, which generalizes the Kolmogorov−Petrovskiy−Piskunov equation. Uniqueness of the Cauchy problem solution was proved and estimates for this solution were obtained.

KEY WORDS: parabolic equation, n-dimensional space, nonlocal nonlinear potential, generalization of the Kolmogorov–Petrovskiy–Piskunov equation, Cauchy problem solution, uniqueness, estimates.

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