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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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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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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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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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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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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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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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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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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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