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A convergent reaction-diffusion master equation [PDF]
Journal of Chemical Physics, 2013 The reaction-diffusion master equation (RDME) is a lattice stochastic reaction-diffusion model that has been used to study spatially distributed cellular processes. The RDME is often interpreted as an approximation to spatially continuous models in which molecules move by Brownian motion and react by one of several mechanisms when sufficiently close ...
Samuel A. Isaacson
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ON REACTION-DIFFUSION EQUATION WITH ABSORPTION
Acta Mathematica Scientia, 1993Summary: We consider the dead core and some asymptotic behaviors of solutions to the initial boundary value problems of the equation \(u_ t= \Delta u- \lambda u^ p e^ u\), where \(\lambda>0 ...
Wang, Liwen, Chen, Qingyi
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On a fractional reaction–diffusion equation
Zeitschrift für angewandte Mathematik und Physik, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
de Andrade, Bruno, Viana, Arlúcio
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Reaction-diffusion equations in immunology
Журнал вычислительной математики и математической физики, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bocharov G.A. +2 more
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EXACT SOLUTIONS OF A REACTION DIFFUSION EQUATION
Asymptotic Methods in Nonlinear Wave Phenomena, 2007A model equation which describes reaction diffusion processes is considered. We classify the possible forms of the material response functions involved in the gov- erning equation under interest allowing generalized separable exact solutions to hold. Exact solutions of a nonlinear second order reaction diffusion equation are calculated.
M. Carini, MANGANARO, Natale
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Reaction–Diffusion Equations and Learning
Journal of Visual Communication and Image Representation, 2002A system of coupled differential equations that learns priors for modeling “preattentive” textures is formulated. Learning is driven by the feature residuals computed from the observed values and the values calculated by the system from a synthesized image that is generated by means of a reaction?diffusion equation.
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Impulsive quenching for reaction—diffusion equations
Nonlinear Analysis: Theory, Methods & Applications, 1994Let \(H= {{\partial^ 2}/{\partial x^ 2}}- {\partial/{\partial t}}\), and \(a\), \(T\) and \(\sigma\) be positive constants. The authors consider the following quenching problem with impulses: for \(n=1,2,3,\dots\), \[ H(u)=- f(u), \qquad ...
Chan, C. Y., Ke, L., Vatsala, A. S.
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Topological techniques in reaction-diffusion equations
Advances in Applied Probability, 1980In this note, we shall illustrate how some topological ideas can be used to obtain rather precise information about solutions of reaction-diffusion equations. The equations are of the form $$ {{\text{u}}_t} = {u_{{xx}}} + {\text{f}}(u), - {\text{L}} < x < {\text{L}} $$ (1) in a single space variable, with either homogeneous Dirichlet or ...
Charles Conley, Joel Smoller
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SPIRALS IN SCALAR REACTION–DIFFUSION EQUATIONS
International Journal of Bifurcation and Chaos, 1995Spiral patterns have been observed experimentally, numerically, and theoretically in a variety of systems. It is often believed that these spiral wave patterns can occur only in systems of reaction–diffusion equations. We show, both theoretically (using Hopf bifurcation techniques) and numerically (using both direct simulation and continuation of ...
Dellnitz, Michael +3 more
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