Results 271 to 280 of about 53,391 (306)

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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A REACTION-DIFFUSION EQUATION ON STRATIFIED GROUPS

Journal of Mathematical Sciences, 2022
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Khumoyun Jabbarkhanov, Joel E. Restrepo, Durvudkhan Suragan   +2 more
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Reaction-Diffusion Equations

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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Periodic Solutions to Reaction-Diffusion Equations

SIAM Journal on Applied Mathematics, 1976
In 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, 1998
In 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, 1997
The 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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On the Existence of Pulses in Reaction- Diffusion- Equations

Results in Mathematics, 1992
The 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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Reaction - diffusion equations in perforated media

Nonlinearity, 1997
The author considers the problem \[ {\partial\over\partial t} u(t,x)= {1\over 2} \sum^r_{i,j= 1} a_{ij}(x){\partial^2\over \partial x_i\partial x_j} u(t,x)+ \sum^r_{i= 1} b_i(x){\partial\over\partial x_i} u(t,x),\;t\in (0,\infty),\;x\in D= \mathbb{R}^r\setminus \bigcup^\infty_{i= 1} H_i, \] \[ {\partial u\over\partial n}+ f(x,u)= 0,\;x\in\bigcup ...
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On the Solution of Reaction—Diffusion Equations

IMA Journal of Applied Mathematics, 1981
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Fast-Diffusion Limit for Reaction–Diffusion Equations with Degenerate Multiplicative and Additive Noise

Journal of Dynamics and Differential Equations, 2020
Wael W Mohammed, Mohammed Wael W
exaly