Fully nonlinear dead-core systems
Dami\~ao J. Ara\'ujo, Rafayel Teymurazyan
TL;DR
This paper investigates fully nonlinear dead-core systems with strong absorption, revealing new regularity, free boundary properties, and Liouville theorems, advancing understanding even in linear cases.
Contribution
It introduces novel regularity results, free boundary coincidence, and Liouville theorems for nonlinear dead-core systems, extending known results to new nonlinear contexts.
Findings
Higher sharp regularity across free boundaries
Geometric measure estimates for free boundary sets
Coincidence of free boundaries in the system
Abstract
We study fully nonlinear dead-core systems coupled with strong absorption terms. We discover a chain reaction, exploiting properties of an equation along the system and obtain higher sharp regularity across the free boundary. Additionally, we prove geometric measure estimates and obtain coincidence of the free boundaries. We also derive Liouville type theorems for entire solutions. These results are new even for linear systems.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Mathematical Biology Tumor Growth · Numerical methods for differential equations