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2014
The reaction-diffusion processes occur in systems comprising particles, atoms or molecules of various types which diffuse and can react with each other. However, we will study only systems constituted by particles of a single type. Thus the possible reaction involve the annihilation or creation of particles of the same type.
Tânia Tomé, Mário J. de Oliveira
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The reaction-diffusion processes occur in systems comprising particles, atoms or molecules of various types which diffuse and can react with each other. However, we will study only systems constituted by particles of a single type. Thus the possible reaction involve the annihilation or creation of particles of the same type.
Tânia Tomé, Mário J. de Oliveira
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1990
Abstract Reaction-diffusion equations form a class of differential equations which in recent years have seen great steps forward both in the understanding of their analytical structure and in their application to a wide variety of scientific phenomena.
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Abstract Reaction-diffusion equations form a class of differential equations which in recent years have seen great steps forward both in the understanding of their analytical structure and in their application to a wide variety of scientific phenomena.
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1992
The method of upper and lower solutions and its associated monotone iteration are introduced for both the time-dependent and the steady-state reaction diffusion equations. Based on the principle of conservation a derivation of the equations, including nonlinear boundary conditions, is given in the general framework of reaction diffusion systems.
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The method of upper and lower solutions and its associated monotone iteration are introduced for both the time-dependent and the steady-state reaction diffusion equations. Based on the principle of conservation a derivation of the equations, including nonlinear boundary conditions, is given in the general framework of reaction diffusion systems.
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2004
We shall consider here a stochastic heat equation pertubed by a polynomial term off odd degree d > 1 having negative leading coefficient (this will ensure non-explosion). We can represent this polynomial as \(\begin{array}{*{20}{c}} {\lambda \xi - p(\xi ),} & {\xi \in \mathbb{R},} \\ \end{array}\) where λ ∈ ℝ and p is an increasing polynomial, that is ...
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We shall consider here a stochastic heat equation pertubed by a polynomial term off odd degree d > 1 having negative leading coefficient (this will ensure non-explosion). We can represent this polynomial as \(\begin{array}{*{20}{c}} {\lambda \xi - p(\xi ),} & {\xi \in \mathbb{R},} \\ \end{array}\) where λ ∈ ℝ and p is an increasing polynomial, that is ...
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2014
This chapter addresses the stochastic dynamics of interacting particle systems, specifically reaction-diffusion models that, for example, capture chemical reactions in a gel such that convective transport is inhibited. Generic reaction-diffusion models are in fact utilized to describe a multitude of phenomena in various disciplines, ranging from ...
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This chapter addresses the stochastic dynamics of interacting particle systems, specifically reaction-diffusion models that, for example, capture chemical reactions in a gel such that convective transport is inhibited. Generic reaction-diffusion models are in fact utilized to describe a multitude of phenomena in various disciplines, ranging from ...
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2000
Reaction-diffusion equations are widely used for modeling chemical reactions, biological systems, population dynamics and nuclear reactor physics. They are of the form $$\frac{{\partial u}}{{\partial t}} = D\Delta u + f(u,\lambda ) $$ (1.1)
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Reaction-diffusion equations are widely used for modeling chemical reactions, biological systems, population dynamics and nuclear reactor physics. They are of the form $$\frac{{\partial u}}{{\partial t}} = D\Delta u + f(u,\lambda ) $$ (1.1)
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Gas diffusion electrodes and membranes for CO2 reduction electrolysers
Nature Reviews Materials, 2021Eric W Lees +2 more
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Patterning Complex Line Motifs in Thin Films Using Immersion‐Controlled Reaction‐Diffusion
Advanced Materials, 2023Christiaan van Campenhout +1 more
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