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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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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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On a fractional reaction–diffusion equation
Zeitschrift für angewandte Mathematik und Physik, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
de Andrade, Bruno, Viana, Arlúcio
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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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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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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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Generalized reaction–diffusion equations
Chemical Physics Letters, 1999Abstract This Letter proposes generalized reaction–diffusion equations for treating noisy magnetic resonance images. An edge-enhancing functional is introduced for image enhancement. A number of super-diffusion operators are introduced for fast and effective smoothing.
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Simulation of nonlinear reaction-diffusion equations
Bulletin of Mathematical Biology, 1977Discrete particle simulation techniques developed for problems in plasma physics have been adapted to investigate one-dimensional dissipative structures. The results of the model are found to be consistent with bifurcation analysis of nonlinear reaction-diffusion equations.
Stetson, R. F. +2 more
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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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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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