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Existence and approximation results for gradient flows

Riccarda Rossi, Giuseppe Savaré (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This note addresses the Cauchy problem for the gradient flow equation in a Hilbert space H u ...

Gradient systems of closed operators

Vittorino Pata (2009)

Open Mathematics

A classical result on the existence of global attractors for gradient systems is extended to the case of a semigroup S(t) lacking strong continuity, but satisfying the weaker property of being a closed map for every fixed t ≥ 0.

Hyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approach

Rachele Foschi (2013)


In previous papers, evolution of dependence and ageing, for vectors of non-negative random variables, have been separately considered. Some analogies between the two evolutions emerge however in those studies. In the present paper, we propose a unified approach, based on semigroup arguments, explaining the origin of such analogies and relations among properties of stochastic dependence and ageing.

Numerical Approximations of the Dynamical System Generated by Burgers’ Equation with Neumann–Dirichlet Boundary Conditions

Edward J. Allen, John A. Burns, David S. Gilliam (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Using Burgers’ equation with mixed Neumann–Dirichlet boundary conditions, we highlight a problem that can arise in the numerical approximation of nonlinear dynamical systems on computers with a finite precision floating point number system. We describe the dynamical system generated by Burgers’ equation with mixed boundary conditions, summarize some of its properties and analyze the equilibrium states for finite dimensional dynamical systems that are generated by numerical approximations of this...

Periodic solutions of dissipative dynamical systems with singular potential and p-Laplacian

Bing Liu (2002)

Annales Polonici Mathematici

By using the topological degree theory and some analytic methods, we consider the periodic boundary value problem for the singular dissipative dynamical systems with p-Laplacian: ( ϕ p ( x ' ) ) ' + d / d t g r a d F ( x ) + g r a d G ( x ) = e ( t ) , x(0) = x(T), x’(0) = x’(T). Sufficient conditions to guarantee the existence of solutions are obtained under no restriction on the damping forces d/dt gradF(x).

Positive periodic solutions of parabolic evolution problems: a translation along trajectories approach

Aleksander Ćwiszewski (2011)

Open Mathematics

A translation along trajectories approach together with averaging procedure and topological degree are used to derive effective criteria for existence of periodic solutions for nonautonomous evolution equations with periodic perturbations. It is shown that a topologically nontrivial zero of the averaged right hand side is a source of periodic solutions for the equations with increased frequencies. Our setting involves equations on closed convex cones, therefore it enables us to study positive solutions...

Semilinear Cauchy Problems with Almost Sectorial Operators

Tomasz Dlotko (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

Existence of a mild solution to a semilinear Cauchy problem with an almost sectorial operator is studied. Under additional regularity assumptions on the nonlinearity and initial data we also prove the existence of a classical solution to this problem. An example of a parabolic problem in Hölder spaces illustrates the abstract result.

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