Necrotic tumor growth: an analytic approach
, 2012 The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium.
A Friedman +14 more
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An Energetic Variational Approach for ion transport
, 2014 The transport and distribution of charged particles are crucial in the study of many physical and biological problems. In this paper, we employ an Energy Variational Approach to derive the coupled Poisson-Nernst-Planck-Navier-Stokes system.
Liu, Chun, Sheng, Ping, Xu, Shixin
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Global-in-time behavior of the solution to a Gierer-Meinhardt system [PDF]
, 2012 Gierer-Meinhardt system is a mathematical model to describe biological pattern formation due to activator and inhibitor. Turing pattern is expected in the presence of local self-enhancement and long-range inhibition.
Karali, Georgia D +2 more
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Boundedness and exponential convergence of a chemotaxis model for tumor invasion
, 2016 We revisit the following chemotaxis system modeling tumor invasion \begin{equation*} \begin{cases} u_t=\Delta u-\nabla \cdot(u\nabla v),& x\in\Omega, t>0,\\ v_t=\Delta v+wz,& x\in\Omega, t>0,\\ w_t=-wz,& x\in\Omega, t>0,\\ z_t=\Delta z-z+u, & x\in\Omega,
Jin, Haiyang, Xiang, Tian
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Phase Transitions for the Brusselator Model
, 2010 Dynamic phase transitions of the Brusselator model is carefully analyzed, leading to a rigorous characterization of the types and structure of the phase transitions of the model from basic homogeneous states.
Ma T., Ma T., Shouhong Wang, Tian Ma
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, 2017 In this paper we study the zero-flux chemotaxis-system \begin{equation*} \begin{cases} u_{ t}=\nabla \cdot ((u+1)^{m-1} \nabla u-(u+1)^\alpha \chi(v)\nabla v) + ku-\mu u^2 & x\in \Omega, t>0, \\ v_{t} = \Delta v-vu & x\in \Omega, t>0,\\ \end{cases} \end ...
Amann +34 more
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Dynamical properties of single species stage structured model with Michaelis-Menten type harvesting on adult population and linear harvesting on juvenile population. [PDF]
Heliyon, 2023 Akter S, Islam MS, Hossain T.
europepmc +1 more source
Steady solution and its stability of a mathematical model of diabetic atherosclerosis. [PDF]
J Biol Dyn, 2023 Xie X.
europepmc +1 more source
Global Dynamics of a Diffusive Two-Strain Epidemic Model with Non-Monotone Incidence Rate. [PDF]
Iran J Sci Technol Trans A Sci, 2022 Khatua A, Pal D, Kar TK.
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Dynamics and calculation of the basic reproduction number for a nonlocal dispersal epidemic model with air pollution. [PDF]
J Appl Math Comput, 2023 Zhou Q, Xu X, Zhang Q.
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