najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2018-9-3-323-329najo-776Research ArticleMATHEMATICSМАТЕМАТИКАOn the behavior of the solution of a nonlinear polytropic filtration problem with a source and multiple nonlinearitiesRakhmonovZ. R.

Universitet, 4, Tashkent, 100174

zraxmonov@inbox.ruTillaevA. I.

Universitet, 4, Tashkent, 100174

tillayev1@mail.ruNational University of Uzbekistan, Applied Mathematics and Computer AnalysisUzbekistan20181408202593323329Copyright © Rakhmonov Z.R., Tillaev A.I., 20252025Rakhmonov Z.R., Tillaev A.I.Rakhmonov Z.R., Tillaev A.I.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/776

In this paper, we study the global solvability and unsolvability conditions of a nonlinear filtration problem with nonlinear boundary flux. We establish the critical global existence exponent and critical Fujita exponent of nonlinear filtration problem in inhomogeneous medium. An asymptotic representation of the solution with a compact support is obtained, which made it possible to carry out a numerical experiment.

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The authors declare that there are no conflicts of interest present.