AN INVERSE PROBLEM FOR THE POROUS MEDIUM EQUATION WITH PARTIAL DATA AND A POSSIBLY SINGULAR ABSORPTION TERM

Cătălin I. Cărstea, Tuhin Ghosh, Gunther Uhlmann

研究成果: Article同行評審

摘要

In this paper we prove uniqueness in the inverse boundary value problem for the three coefficient functions in the porous medium equation with an absorption term є∂tu - ∇ ∙ (γ∇um) + λuq = 0 with m > 1, m -1 < q < √m, with the space dimension 2 or higher. This is a degenerate parabolic type quasilinear PDE which has been used as a model for phenomena in fields such as gas flow (through a porous medium), plasma physics, and population dynamics. In the case when γ = 1 a priori, we prove unique identifiability with data supported in an arbitrarily small part of the boundary. Even for the global problem we improve on previous work by obtaining uniqueness with a finite (rather than infinite) time of observation and also by introducing the additional absorption term λuq.

原文English
頁(從 - 到)162-185
頁數24
期刊SIAM Journal on Mathematical Analysis
55
發行號1
DOIs
出版狀態Published - 2月 2023

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