Results 251 to 260 of about 4,210,778 (298)

Reaction-diffusion equations in immunology

Журнал вычислительной математики и математической физики, 2018
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Bocharov G.A., Volpert V.A., Tasevich A.L.   +2 more
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EXACT SOLUTIONS OF A REACTION DIFFUSION EQUATION

Asymptotic Methods in Nonlinear Wave Phenomena, 2007
A 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, 2002
A 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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Solving linear and non-linear space–time fractional reaction–diffusion equations by the Adomian decomposition method

International Journal for Numerical Methods in Engineering, 2008
In this paper, we consider linear and non-linear space-time fractional reaction-diffusion equations (STFRDE) on a finite domain. The equations are obtained from standard reaction-diffusion equations by replacing a second-order space derivative by a ...
Qiang Yu, Fawang Liu, Vo Anh
exaly   +2 more sources

Impulsive quenching for reaction—diffusion equations

Nonlinear Analysis: Theory, Methods & Applications, 1994
Let \(H= {{\partial^ 2}/{\partial x^ 2}}- {\partial/{\partial t}}\), 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, 1980
In 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, 1995
Spiral 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, Golubitsky, Martin, Hohmann, Andreas, Stewart, Ian   +3 more
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Phaselocking in a Reaction-Diffusion Equation with Twist

SIAM Journal on Mathematical Analysis, 1994
In two previous papers [SIAM J. Appl. Math. 46, 359-367 (1986; Zbl 0606.92012); SIAM J. Math. Anal. 20, No. 6, 1436-1446 (1989; Zbl 0701.35019)] we have analyzed continuous diffusion models of coupled oscillators for a special class of reaction-diffusion equations.
Ermentrout, G. Bard, Troy, W. C.
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Stationary solutions of reaction‐diffusion equations

Mathematical Methods in the Applied Sciences, 1979
AbstractGiven a semilinear reaction‐diffusion equation. If the corresponding ordinary differential equation admits a convex compact positively invariant set and the boundary data assume their values in this set then the first and third boundary value problem have stationary solutions.
Hadeler, K. P., Rothe, F., Vogt, H.
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Exact Solutions of Reaction-Diffusion Equation

Journal of the Physical Society of Japan, 1993
Summary: The statitical interactions of anyons on a plane are described by a gauge field. We present a natural periodic generalization of such gauge field and find that this agrees with the corresponding gauge field on a torus which has been obtained from the Chern-Simons theory.
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