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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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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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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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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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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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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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Nonlocal reaction—diffusion equations and nucleation
IMA Journal of Applied Mathematics, 1992Summary: A nonlocal reaction-diffusion equation is presented and analysed using matched asymptotic expansions and multiple timescales. The problem models a binary mixture undergoing phase separation. The particular form of the equation is motivated by arguments from the calculus of variations, with the nonlocality arising from an enforcement of ...
Rubinstein, Jacob, Sternberg, Peter
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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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On a time fractional reaction diffusion equation
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bashir Ahmad 0003 +4 more
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Adaptive FEM for reaction—diffusion equations
Applied Numerical Mathematics, 1998In the first part of the paper the author shortly presents some methods for solving mixed systems of nonlinear parabolic and elliptic differential equations. Especially a short comparison between the adaptive method of lines and Rothe's approach is presented. Then the author describes the time integrator and the finite element method (FEM) derived from
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