FREE BOUNDARY PROBLEM FOR A QUASILINEAR PARABOLIC EQUATION WITH A NONLOCAL BOUNDARY CONDITION
J.O. Takhirov, B.B. Anvarjonov
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Source: Crossref
Published: Dec 1, 2023
DOI: 10.29229/uzmj.2023-4-10
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We study a diffusion logistic model with a free boundary and a nonlocal condition on a fixed boundary. Problem dynamics are examined to describe the spread of new or invasive species when the unknown boundary represents an expanding front. A priori estimates of Schauder type are established, on the basis of which the unique global solvability of the problem is proved. Some properties of the solution are investigated.
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