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Prescribed-time H1-stabilization of reaction-diffusion equations by means of output feedback
European Control Conference, 2019We study the problem of stabilizing reaction-diffusion equations within a prescribed time. We employ the backstepping method and select a target equation whose state and its spatial derivative converge to zero within the prescribed time.
D. Steeves, M. Krstić, R. Vázquez
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Reaction-diffusion equations in immunology
Журнал вычислительной математики и математической физики, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bocharov G.A. +2 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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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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Reaction–diffusion equation based image restoration
Applied Mathematics and Computation, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhao, Xueqing +6 more
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ON REACTION-DIFFUSION EQUATION WITH ABSORPTION
Acta Mathematica Scientia, 1993Summary: We consider the dead core and some asymptotic behaviors of solutions to the initial boundary value problems of the equation \(u_ t= \Delta u- \lambda u^ p e^ u\), where \(\lambda>0 ...
Wang, Liwen, Chen, Qingyi
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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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Introduction to Reaction-Diffusion Equations
Lecture Notes on Mathematical Modelling in the Life Sciences, 2022King-Yeung Lam, Y. Lou
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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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