166 citations · 316 across the 24 of their papers we have counts for
14 papers · 1 filter
Tumor boundary instability induced by nutrient consumption and supply
Yu Feng, Min Tang, Xiaoqian Xu +1
We investigate the tumor boundary instability induced by nutrient consumption and supply based on a Hele-Shaw model derived from taking the incompressible limit of a cell density m…
Kinetic chemotaxis tumbling kernel determined from macroscopic quantities
Kathrin Hellmuth, Christian Klingenberg, Qin Li +1
Chemotaxis is the physical phenomenon that bacteria adjust their motions according to chemical stimulus. A classical model for this phenomenon is a kinetic equation that describes…
Multiscale convergence of the inverse problem for chemotaxis in the Bayesian setting
Kathrin Hellmuth, Christian Klingenberg, Qin Li +1
Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe th…
On kinetic and macroscopic models for the stripe formation in engineered bacterial populations
Ning Jiang, Jiangyan Liang, Yi-Long Luo +2
We study the well-posedness of the biological models with AHL-dependent cell mobility on engineered Escherichia coli populations. For the kinetic model proposed by Xue-Xue-Tang rec…
Mathematical Modelling and Analysis of Fractional Diffusion Induced by Intracellular Noise
Weiran Sun, Min Tang, Xiaoru Xue
In this paper we use an individual-based model and its associated kinetic equation to study the generation of long jumps in the motion of E. coli. These models relate the run-and-t…
Towards understanding the boundary propagation speeds in tumor growth models
Jian-Guo Liu, Min Tang, Li Wang +1
At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific…
Multiple asymptotics of Kinetic Equations with Internal States
Benoit Perthame, Weiran Sun, Min Tang +1
The run and tumble process is well established in order to describe the movement of bacteria in response to a chemical stimulus. However the relation between the tumbling rate and…
Analysis and computation of some tumor growth models with nutrient: from cell density models to free boundary dynamics
Jian-Guo Liu, Min Tang, Li Wang +1
In this paper, we study the tumor growth equation along with various models for the nutrient component, including the \emph{in vitro} model and the \emph{in vivo} model. At the cel…
The fractional diffusion limit of a kinetic model with biochemical pathway
Benoît Perthame, Weiran Sun, Min Tang
Kinetic-transport equations that take into account the intra-cellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathe…
Macroscopic limits of pathway-based kinetic models for E.coli chemotaxis in large gradient environments
Weiran Sun, Min Tang
It is of great biological interest to understand the molecular origins of chemotactic behavior of E. coli by developing population-level models based on the underlying signaling pa…
Well-balanced and asymptotic preserving schemes for kinetic models
Casimir Emako, Min Tang
In this paper, we propose a general framework for designing numerical schemes that have both well-balanced (WB) and asymptotic preserving (AP) properties, for various kinds of kine…
Derivation of the bacterial run-and-tumble kinetic equation from a model with biochemical pathway
Benoît Perthame, Min Tang, Nicolas Vauchelet
Kinetic-transport equations are, by now, standard models to describe the dynamics of populations of bacteria moving by run-and-tumble. Experimental observations show that bacteria…
Traveling wave solution of the Hele-Shaw model of tumor growth with nutrient
Benoît Perthame, Min Tang, Nicolas Vauchelet
Several mathematical models of tumor growth are now commonly used to explain medical observations and predict cancer evolution based on images. These models incorporate mechanical…
Derivation of a Hele-Shaw type system from a cell model with active motion
Benoît Perthame, Fernando Quirós, Min Tang +1
We formulate a Hele-Shaw type free boundary problem for a tumor growing under the combined effects of pressure forces, cell multiplication and active motion, the latter being the n…