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Antiperiodic Problems for Nonautonomous Parabolic Evolution Equations
"... This work focuses on the antiperiodic problem of nonautonomous semilinear parabolic evolution equation in the form ( ) = ( ) ( ) + ( , ( )), ∈ R, ( + ) = − ( ), ∈ R, where ( ( )) ∈R (possibly unbounded), depending on time, is a family of closed and densely defined linear operators on a Banach space ..."
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This work focuses on the antiperiodic problem of nonautonomous semilinear parabolic evolution equation in the form ( ) = ( ) ( ) + ( , ( )), ∈ R, ( + ) = − ( ), ∈ R, where ( ( )) ∈R (possibly unbounded), depending on time, is a family of closed and densely defined linear operators on a Banach
Variable structure control for parabolic evolution equations
, 2008
"... In this paper it is considered a class of infinitedimensional control systems in a variational setting. By using a FaedoGalerkin method, a sequence of approximating finite dimensional controlled differential equations is defined. On each of these systems a variable structure control is applied to ..."
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to constrain the motion on a specified surface. Under some growth assumptions the convergence of these approximations to an ideal sliding state for the infinitedimensional system is shown. Results are then applied to the Neumann boundary control of a parabolic evolution equation. 1
Spacetime isogeometric analysis of parabolic evolution equations
, 2015
"... We present and analyze a new stable spacetime Isogeometric Analysis (IgA) method for the numerical solution of parabolic evolution equations in fixed and moving spatial computational domains. The discrete bilinear form is elliptic on the IgA space with respect to a discrete energy norm. This pro ..."
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We present and analyze a new stable spacetime Isogeometric Analysis (IgA) method for the numerical solution of parabolic evolution equations in fixed and moving spatial computational domains. The discrete bilinear form is elliptic on the IgA space with respect to a discrete energy norm
Analyticity Of Solutions To Fully Nonlinear Parabolic Evolution Equations On Symmetric Spaces
 J. Evol. Equs
"... It is shown that solutions to fully nonlinear parabolic evolution equations on symmetric Riemannian manifolds are real analytic in space and time, provided the propagator is compatible with the underlying Lie structure. ..."
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Cited by 9 (6 self)
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It is shown that solutions to fully nonlinear parabolic evolution equations on symmetric Riemannian manifolds are real analytic in space and time, provided the propagator is compatible with the underlying Lie structure.
ON QUASILINEAR PARABOLIC EVOLUTION EQUATIONS IN WEIGHTED LpSPACES
, 909
"... Abstract. In this paper we develop a geometric theory for quasilinear parabolic problems in weighted Lpspaces. We prove existence and uniqueness of solutions as well as the continuous dependence on the initial data. Moreover, we make use of a regularization effect for quasilinear parabolic equation ..."
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Cited by 15 (6 self)
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Abstract. In this paper we develop a geometric theory for quasilinear parabolic problems in weighted Lpspaces. We prove existence and uniqueness of solutions as well as the continuous dependence on the initial data. Moreover, we make use of a regularization effect for quasilinear parabolic
Parabolic Evolution Equations With Asymptotically Autonomous Delay
 Report No.2, Fachbereich Mathematik und Informatik, Universitat
, 2001
"... . We study retarded parabolic nonautonomous evolution equations whose coefficients converge as t ! 1 such that the autonomous problem in the limit has an exponential dichotomy. Then the nonautonomous problem inherits the exponential dichotomy and the solution of the inhomogeneous equation ten ..."
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Cited by 6 (4 self)
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. We study retarded parabolic nonautonomous evolution equations whose coefficients converge as t ! 1 such that the autonomous problem in the limit has an exponential dichotomy. Then the nonautonomous problem inherits the exponential dichotomy and the solution of the inhomogeneous equation
A Stable and Accurate Explicit Scheme for Parabolic Evolution Equations
"... We show that the combination of several numerical techniques, including multiscale preconditionning and Richardson extrapolation, yields stable and accurate explicit schemes with large time steps for parabolic evolution equations. Our theoretical study is limited here to linear problems (typically t ..."
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Cited by 2 (0 self)
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We show that the combination of several numerical techniques, including multiscale preconditionning and Richardson extrapolation, yields stable and accurate explicit schemes with large time steps for parabolic evolution equations. Our theoretical study is limited here to linear problems (typically
Heat Kernels and maximal L^p  L^q Estimates for Parabolic Evolution Equations
"... Let A be the generator of an analytic semigroup T on L²(Ω), where Ω is a homogeneous space with doubling property. We prove maximal L p \Gamma L q apriori estimates for the solution of the parabolic evolution equation u 0 (t) = Au(t) + f(t); u(0) = 0 provided T may be represented by a heatk ..."
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Cited by 22 (2 self)
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Let A be the generator of an analytic semigroup T on L²(Ω), where Ω is a homogeneous space with doubling property. We prove maximal L p \Gamma L q apriori estimates for the solution of the parabolic evolution equation u 0 (t) = Au(t) + f(t); u(0) = 0 provided T may be represented by a heat
Probabilistic approximation via spatial derivation of some nonlinear parabolic evolution equations
 In Monte Carlo and QuasiMonte Carlo Methods 2004 197–216
, 2006
"... Summary. For some parabolic equations with a local nonlinearity, a suitable spatial derivation leads to a FokkerPlanck equation with a nonlocal nonlinearity. In this paper we present a review of the particle methods obtained by replacing the nonlinearity in this FokkerPlanck equation by interacti ..."
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Cited by 2 (2 self)
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Summary. For some parabolic equations with a local nonlinearity, a suitable spatial derivation leads to a FokkerPlanck equation with a nonlocal nonlinearity. In this paper we present a review of the particle methods obtained by replacing the nonlinearity in this FokkerPlanck equation
Results 1  10
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16,936