Results 261 to 270 of about 4,210,778 (298)
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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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Periodic Solutions to Reaction-Diffusion Equations
SIAM Journal on Applied Mathematics, 1976In this note we derive asymptotic formulas for rotating-spiral and axisymmetric, time-periodic solutions to reaction-diffusion systems.
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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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Travelling Waves for Reaction Diffusion Equations
Journal of Partial Differential Equations, 1997The paper deals with the travelling wave solution \(u(x,t)=u(x+kt)\) \((k>0)\) of the reaction diffusion equation: \[ u_t=u_{xx}+f(x),\quad u(+\infty)=H\quad\text{and }u(-\infty)=0\quad\text{for some }H>0, \] where the nonlinear term \(f(u)\) is assumed to be Lipschitz continuous and to satisfy \(f(0)=f(H)=0\) and \(\int^H_0f(s)ds>0\).
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