The Experts below are selected from a list of 20964 Experts worldwide ranked by ideXlab platform
Nicolas Vauchelet - One of the best experts on this subject based on the ideXlab platform.
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Traveling Wave Solution of the hele shaw model of tumor growth with nutrient
Mathematical Models and Methods in Applied Sciences, 2014Co-Authors: Benoit Perthame, Min Tang, Nicolas VaucheletAbstract: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 laws for tissue compression combined with rules for nutrients availability which can differ depending on the situation under consideration, in vivo or in vitro. Numerical Solutions exhibit, as expected from medical observations, a proliferative rim and a necrotic core. However, their precise profiles are rather complex, both in one and two dimensions. We study a simple free boundary model formed of a Hele–Shaw equation for the cell number density coupled to a diffusion equation for a nutrient. We can prove that a Traveling Wave Solution exists with a healthy region separated from the progressing tumor by a sharp front (the free boundary) while the transition to the necrotic core is smoother. Remarkable is the pressure distribution which vanishes at the boundary of the proliferative rim with a vanishing derivative at the transition point to the necrotic core.
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Traveling Wave Solution of the hele shaw model of tumor growth with nutrient
arXiv: Analysis of PDEs, 2014Co-Authors: Benoit Perthame, Min Tang, Nicolas VaucheletAbstract: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 laws for tissue compression combined with rules for nutrients availability which can differ depending on the situation under consideration, in vivo or in vitro. Numerical Solutions exhibit, as expected from medical observations, a proliferative rim and a necrotic core. However, their precise profiles are rather complex, both in one and two dimensions.
Zengji Du - One of the best experts on this subject based on the ideXlab platform.
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Traveling Wave Solution of a reaction diffusion predator prey system
Qualitative Theory of Dynamical Systems, 2019Co-Authors: Dongcheng Xu, Zengji DuAbstract:In this paper, we discuss a reaction–diffusion predator–prey model with nonlocal delays. By using the theory of dynamical systems, specifically based on geometric singular perturbation theory, center manifold theorem and Fredholm theory, we construct an invariant manifold for the associated predator–prey equation and use this invariant manifold to obtain a heteroclinic orbit between two non-negative equilibrium points. Furthermore, we establish the existence result of Traveling Wave Solution for the predator–prey model.
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Traveling Wave Solutions of a reaction-diffusion predator-prey model
Discrete and Continuous Dynamical Systems - Series S, 2017Co-Authors: Xiaohui Shang, Zengji DuAbstract:This paper is concerned with the dynamics of Traveling Wave Solutions for a reaction-diffusion predator-prey model with a nonlocal delay. By using Schauder's fixed point theorem, we establish the existence result of a Traveling Wave Solution connecting two steady states by constructing a pair of upper-lower Solutions which are easy to construct in practice. We also investigate the asymptotic behavior of Traveling Wave Solutions by employing the standard asymptotic theory.
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Traveling Wave Solution for a reaction diffusion competitive cooperative system with delays
Boundary Value Problems, 2016Co-Authors: Zengji Du, Dongcheng XuAbstract:This paper investigates the existence of Traveling Wave Solution to a three species reaction-diffusion system with delays, which includes competitive relationship, cooperative relationship and predator-prey relationship. By using the method of upper-lower Solutions, the cross iteration method and Schauder’s fixed point theorem, the existence of a Traveling Wave Solution is obtained.
Benoit Perthame - One of the best experts on this subject based on the ideXlab platform.
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Traveling Wave Solution of the hele shaw model of tumor growth with nutrient
Mathematical Models and Methods in Applied Sciences, 2014Co-Authors: Benoit Perthame, Min Tang, Nicolas VaucheletAbstract: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 laws for tissue compression combined with rules for nutrients availability which can differ depending on the situation under consideration, in vivo or in vitro. Numerical Solutions exhibit, as expected from medical observations, a proliferative rim and a necrotic core. However, their precise profiles are rather complex, both in one and two dimensions. We study a simple free boundary model formed of a Hele–Shaw equation for the cell number density coupled to a diffusion equation for a nutrient. We can prove that a Traveling Wave Solution exists with a healthy region separated from the progressing tumor by a sharp front (the free boundary) while the transition to the necrotic core is smoother. Remarkable is the pressure distribution which vanishes at the boundary of the proliferative rim with a vanishing derivative at the transition point to the necrotic core.
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Traveling Wave Solution of the hele shaw model of tumor growth with nutrient
arXiv: Analysis of PDEs, 2014Co-Authors: Benoit Perthame, Min Tang, Nicolas VaucheletAbstract: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 laws for tissue compression combined with rules for nutrients availability which can differ depending on the situation under consideration, in vivo or in vitro. Numerical Solutions exhibit, as expected from medical observations, a proliferative rim and a necrotic core. However, their precise profiles are rather complex, both in one and two dimensions.
R Peschanski - One of the best experts on this subject based on the ideXlab platform.
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Traveling Wave Solution of the reggeon field theory eps proceedings
arXiv: High Energy Physics - Phenomenology, 2009Co-Authors: R PeschanskiAbstract:We identify the nonlinear evolution equation in impact-parameter space for the "Supercritical Pomeron" in Reggeon Field Theory as a 2-dimensional stochastic Fisher and Kolmogorov-Petrovski-Piscounov equation. It exactly preserves unitarity and leads in its radial form to an high energy Traveling Wave Solution corresponding to an "universal" behavior of the impact-parameter front profile of the elastic amplitude; Its rapidity dependence and form depend only on one parameter, the noise strength, independently of the initial conditions and of the non-linear terms restoring unitarity. Theoretical predictions are presented for the three typical different regimes corresponding to zero, weak and strong noise, respectively. They have phenomenological implications for total and differential hadronic cross-sections at colliders.
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Traveling Wave Solution of the reggeon field theory
Physical Review D, 2009Co-Authors: R PeschanskiAbstract:We identify the nonlinear evolution equation in impact-parameter space for the 'Supercritical Pomeron' in Reggeon field theory as a two-dimensional stochastic Fisher-Kolmogorov-Petrovski-Piscounov equation. It exactly preserves unitarity and leads in its radial form to a high-energy Traveling Wave Solution corresponding to a 'universal' behavior of the impact-parameter front profile of the elastic amplitude; its rapidity dependence and form depend only on one parameter, the noise strength, independently of the initial conditions and of the nonlinear terms restoring unitarity. Theoretical predictions are presented for the three typical distinct regimes corresponding to zero, weak, and strong noise.
Dongcheng Xu - One of the best experts on this subject based on the ideXlab platform.
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Traveling Wave Solution of a reaction diffusion predator prey system
Qualitative Theory of Dynamical Systems, 2019Co-Authors: Dongcheng Xu, Zengji DuAbstract:In this paper, we discuss a reaction–diffusion predator–prey model with nonlocal delays. By using the theory of dynamical systems, specifically based on geometric singular perturbation theory, center manifold theorem and Fredholm theory, we construct an invariant manifold for the associated predator–prey equation and use this invariant manifold to obtain a heteroclinic orbit between two non-negative equilibrium points. Furthermore, we establish the existence result of Traveling Wave Solution for the predator–prey model.
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Traveling Wave Solution for a reaction diffusion competitive cooperative system with delays
Boundary Value Problems, 2016Co-Authors: Zengji Du, Dongcheng XuAbstract:This paper investigates the existence of Traveling Wave Solution to a three species reaction-diffusion system with delays, which includes competitive relationship, cooperative relationship and predator-prey relationship. By using the method of upper-lower Solutions, the cross iteration method and Schauder’s fixed point theorem, the existence of a Traveling Wave Solution is obtained.
