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Phaselocking in a Reaction-Diffusion Equation with Twist
SIAM Journal on Mathematical Analysis, 1994In 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, 1979AbstractGiven 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, 1993Summary: 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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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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An investigation of chaos in reaction‐diffusion equations
Numerical Methods for Partial Differential Equations, 1987AbstractThe purpose of this article is to investigate graphically and numerically the topic of chaos in reaction‐diffusion equations. This article is based on the article by Mitchell and Bruch [1]. One‐ and two‐dimensional forms of the reaction‐diffusion equation are discretized using the explicit Euler finite difference scheme.
Wachholz, James J., Bruch, John C. jun.
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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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Spiral Waves in Reaction-Diffusion Equations
SIAM Journal on Applied Mathematics, 1982We consider the reaction-diffusion system \[\begin{gathered} R_T = \nabla ^2 R + R\left( {1 - R^2 - \vec \nabla \theta \cdot \vec \nabla \theta } \right), \hfill \\ R\theta _T = R\nabla ^2 \theta + 2\vec \nabla R \cdot \vec \nabla \theta + qR^3 \hfill \\ \end{gathered} \]This system governs the solutions of reaction-diffusion systems near a Hopf ...
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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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On the Existence of Pulses in Reaction- Diffusion- Equations
Results in Mathematics, 1992The author applies the theory of invariant manifolds for singularly perturbed ordinary differential equations and results about the persistence of homoclinic orbits in autonomous differential systems with several parameters in order to establish the existence of pulses in reaction-diffusion systems. Essential assumptions for the existence of pulses are
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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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