5 papers
Well-posedness of a Hele-Shaw problem in general dimensions
Olga Turanova, Yuming Paul Zhang
We investigate a Hele-Shaw type free boundary problem in general spatial dimension. We establish a comparison principle and well-posedness for the problem using a notion of viscosi…
Chemotaxis Models with Nonlinear/Porous Medium Diffusion, Consumption, and Logistic source on : I. Global Solvability and Boundedness
Zulaihat Hassan, Wenxian Shen, Yuming Paul Zhang
This series of papers is concerned with the global solvability, boundedness, regularity, and uniqueness of weak solutions to the following parabolic-parabolic chemotaxis system wit…
A Hele-Shaw problem with interior and free boundary oscillation: well-posedness and homogenization
Olga Turanova, Yuming Paul Zhang
We investigate a Hele-Shaw type free boundary problem in one spatial dimension, where heterogeneities appear both on the free boundary and within the interior of the positivity set…
The spreading of global solutions of chemotaxis systems with logistic source and consumption on
Zulaihat Hassan, Wenxian Shen, Yuming Paul Zhang
This paper investigates the spreading properties of globally defined bounded positive solutions of a chemotaxis system featuring a logistic source and consumption: \[ \left\{ \begi…
Global existence of classical solutions of chemotaxis systems with logistic source and consumption or linear signal production on
Zulaihat Hassan, Wenxian Shen, Yuming Paul Zhang
While much literature on chemotaxis systems focuses on bounded domains, this paper emphasizes the global existence of classical solutions for three primary chemotaxis systems with…