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The Geometry of Dissipative Evolution Equations: The Porous Medium Equation
"... We show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural. In order to convince the reader that it is mathematically natural, we show the time asymptotic behavior can be easily understood in this framework. We use the intuition and the ..."
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Cited by 413 (11 self)
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We show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural. In order to convince the reader that it is mathematically natural, we show the time asymptotic behavior can be easily understood in this framework. We use the intuition
Existence, Stability and Blow–up for Dissipative Evolution Equations
"... The problem of stability and blow–up for dissipative evolution equations will be treated by Lyapunov–type methods. The discussion will be carried out particularly in the context of evolution operators in a Banach space, with special care given to an appropriate definition of solution, and with the s ..."
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The problem of stability and blow–up for dissipative evolution equations will be treated by Lyapunov–type methods. The discussion will be carried out particularly in the context of evolution operators in a Banach space, with special care given to an appropriate definition of solution
Unconditional convergence of DIRK schemes applied to dissipative evolution equationsI
"... In this paper we prove the convergence of algebraically stable DIRK schemes applied to dissipative evolution equations on Hilbert spaces. The convergence analysis is unconditional as we do not impose any restrictions on the initial value or assume any extra regularity of the solution. The analysis i ..."
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In this paper we prove the convergence of algebraically stable DIRK schemes applied to dissipative evolution equations on Hilbert spaces. The convergence analysis is unconditional as we do not impose any restrictions on the initial value or assume any extra regularity of the solution. The analysis
RUNGEKUTTA TIME DISCRETIZATIONS OF NONLINEAR DISSIPATIVE EVOLUTION EQUATIONS
"... Abstract. Global error bounds are derived for RungeKutta time discretizations of fully nonlinear evolution equations governed by mdissipative vector fields on Hilbert spaces. In contrast to earlier studies, the analysis presented here is not based on linearization procedures, but on the fully nonl ..."
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Cited by 4 (1 self)
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Abstract. Global error bounds are derived for RungeKutta time discretizations of fully nonlinear evolution equations governed by mdissipative vector fields on Hilbert spaces. In contrast to earlier studies, the analysis presented here is not based on linearization procedures, but on the fully
DYNAMICS OF TRAJECTORIES AND THE FINITEDIMENSIONAL REDUCTION OF DISSIPATIVE EVOLUTION EQUATIONS
"... Abstract: We consider a general class of evolution equations with nonlinear dissipation. Under minimal regularity assumptions, we show that the largetime dynamics can be uniquely described by a system of ODEs with infinite, but exponentially decaying memory. The existence of a finitedimensional at ..."
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Abstract: We consider a general class of evolution equations with nonlinear dissipation. Under minimal regularity assumptions, we show that the largetime dynamics can be uniquely described by a system of ODEs with infinite, but exponentially decaying memory. The existence of a finite
equations the porous medium equation
"... The geometry of dissipative evolution equations the porous medium equation by ..."
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The geometry of dissipative evolution equations the porous medium equation by
Asymptotic behavior of secondorder dissipative evolution equations combining potential with nonpotential effects, ESAIM: Control, Optimisation and Calculus of Variations
, 2010
"... Abstract. In the setting of a real Hilbert space H, we investigate the asymptotic behavior, as time t goes to infinity, of trajectories of secondorder evolution equations ü(t) + γu̇(t) +∇φ(u(t)) + A(u(t)) = 0, where∇φ is the gradient operator of a convex differentiable potential function φ: H → R ..."
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Cited by 3 (0 self)
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Abstract. In the setting of a real Hilbert space H, we investigate the asymptotic behavior, as time t goes to infinity, of trajectories of secondorder evolution equations ü(t) + γu̇(t) +∇φ(u(t)) + A(u(t)) = 0, where∇φ is the gradient operator of a convex differentiable potential function φ: H
Evolution of indirect reciprocity by image scoring, Nature
, 1998
"... review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work. IIASA STUDIES IN ADAPTIVE DYNAMICS NO. 27 The Adaptive Dynamics Network at IIASA fosters the development of new mathematical ..."
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Cited by 486 (16 self)
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and conceptual techniques for understanding the evolution of complex adaptive systems. Focusing on these longterm implications of adaptive processes in systems of limited growth, the Adaptive Dynamics Network brings together scientists and institutions from around the world with IIASA acting as the central node
Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics
 J. Geophys. Res
, 1994
"... . A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The ..."
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Cited by 782 (22 self)
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covariance equation are avoided because storage and evolution of the error covariance matrix itself are not needed. The results are also better than what is provided by the extended Kalman filter since there is no closure problem and the quality of the forecast error statistics therefore improves. The method
Elastically deformable models
 Computer Graphics
, 1987
"... The goal of visual modeling research is to develop mathematical models and associated algorithms for the analysis and synthesis of visual information. Image analysis and synthesis characterize the domains of computer vision and computer graphics, respectively. For nearly three decades, the vision an ..."
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Cited by 880 (19 self)
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to control the creation and evolution of models. Mathematically, the approach prescribes systems of dynamic (ordinary and partial) differential equations to govern model behavior. These equations of motion may be
Results 1  10
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775,036