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A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems
(Ele-Math, 2009-08)
In this paper we present a generalization of the Kalman rank condition for linear ordinary differential systems to the case of systems of n coupled parabolic equations (posed in the time interval (0,T) with T > 0) where ...
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Existence and Uniqueness of Solutions for Non-Linear Stochastic Partial Differential Equations
(1991)
We state some results on existence and uniqueness for the solution of non linear stochastic PDEs with deviating arguments. In fact, we consider the equation dx(t) + (A(t; x(t)) + B(t; x(¿ (t))) + f(t)) dt = (C(t; x(½(t))) ...
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A new algorithm of proper generalized decomposition for parametric symmetric elliptic problems
(Society for Industrial and Applied Mathematics, 2018)
We introduce a new algorithm of proper generalized decomposition (PGD) for parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most ...
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Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations
(IOP Publishing, 2017-01)
The global attractor of a skew product semiflow for a non-autonomous differential equation describes the asymptotic behaviour of the model. This attractor is usually characterized as the union, for all the parameters in ...
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Attractors for locally damped Bresse systems and a unique continuation property
(Cornell University, 2021-02-24)
This paper is devoted to Bresse systems, a robust model for circular beams, given by a set of three coupled wave equations. The main objective is to establish the existence of global attractors for dynamics of semilinear ...
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Attractors for Parametric Delay Differential Equations Without Uniqueness and Their Upper Semicontinuous Behaviour
(Elsevier, 2008)
We prove existence of a global attractor A(λ) under minimal assumptions for a general class of parameterized delay differential equations without uniqueness and posed in potentially different state spaces. Secondly, we ...
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Statistical solutions and piecewise Liouville theorem for the impulsive reaction-diffusion equations on in nite lattices
(Elsevier, 2021-04-05)
We first verify the global well-posedness of the impulsive reaction-diffusion equations on infinite lattices. Then we establish that the generated process by the solution operators has a pullback attractor and a family of ...
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The differentiability of the drag with respect to the variations of a Lipschitz domain in a Navier-Stokes flow
(Society for Industrial and Applied Mathematics, 1997)
This paper is concerned with the computation of the drag T associated with a body traveling at uniform velocity in a fluid governed by the stationary Navier–Stokes equations. It is assumed that the fluid fills a domain of ...
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Pullback exponential attractors for differential equations with delay
(American Institute of Mathematical Sciences, 2021-01-01)
We show the existence of an exponential attractor for non-autono-mous dynamical system with bounded delay. We considered the case of strong dissipativity then prove that the result remains for the weak dissipativity. We ...