Archivio della ricerca dell'Università di Modena e Reggio Emiliahttps://iris.unimore.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Wed, 17 Jul 2019 23:04:58 GMT2019-07-17T23:04:58Z10451A doubly nonlinear parabolic equation with a singular potentialhttp://hdl.handle.net/11380/616695Titolo: A doubly nonlinear parabolic equation with a singular potential
Abstract: Our aim in this paper is to study the long time behavior, in termsof finite dimensional attractors, of doubly nonlinear Allen-Cahntype equations with singular potentials.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11380/6166952011-01-01T00:00:00ZFINITE DIMENSIONAL ATTRACTORS FOR THE CAGINALPSYSTEM WITH SINGULAR POTENTIALS ANDDYNAMIC BOUNDARY CONDITIONShttp://hdl.handle.net/11380/615875Titolo: FINITE DIMENSIONAL ATTRACTORS FOR THE CAGINALPSYSTEM WITH SINGULAR POTENTIALS ANDDYNAMIC BOUNDARY CONDITIONS
Abstract: Our aim in this paper is to prove the existence of finite dimensional attractors forthe Caginalp system with dynamic boundary conditions and singular potentials.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11380/6158752009-01-01T00:00:00ZOn the hyperbolic relaxation of the one-dimensional Cahn-Hilliard equationhttp://hdl.handle.net/11380/453670Titolo: On the hyperbolic relaxation of the one-dimensional Cahn-Hilliard equation
Abstract: We consider the one-dimensional Cahn-Hilliard equation with aninertial term ε∂_tt u, for ε ≥ 0. This equation, endowed with proper boundary conditions, generates a strongly continuous semigroup S_ε(t) which acts on a suitable phase-space and possesses a global attractor. Our main result is the construction of a robust family of exponential attractors M_ε, whose common basins of attraction are the whole phase-space.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11380/4536702005-01-01T00:00:00ZSolvability of a plane elliptic problem for the flow in a channel with a surface-piercing obstaclehttp://hdl.handle.net/11380/453679Titolo: Solvability of a plane elliptic problem for the flow in a channel with a surface-piercing obstacle
Abstract: Let us consider the three-dimensional problem of the steady flow of a heavy ideal fluid past a surface-piercing obstacle in a rectangular channel of constant depth. The flow is parallel at infinity upstream, with constant velocity c. We discuss an approximate linear problem obtained in the limit of a "flat obstacle". This is a boundary value problem for the Laplace equation in a three-dimensional unbounded domain, with a second order condition on part of the boundary, the Neumann-Kelvin condition. By a Fourier expansion of the potential function, we reduce the three-dimensional problem to a sequence of plane problems for the Fourier coefficients; for every value of the velocity c, these problems can be described in terms of a two parameter elliptic problem in a strip. We discuss the two dimensional problem by a special variational approach, relying on some a priori properties of finite energy solutions; as a result, we prove unique solvability for 〖c≠c〗_(m,k) where c_(m,k) is a known sequence of values depending on the dimensions of the channel and on the limit length of the obstacle. Accordingly, we can prove the existence of a solution of the three-dimensional problem; the related flow has in general a non trivial wave pattern at infinity downstream. We also investigate the regularity of the solution in a neighborhood of the obstacle. The meaning of the singular values c_(m,k) is discussed from the point of view of the nonlinear theory.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/11380/4536792003-01-01T00:00:00ZCorrigendum to"Existence of global solutions to the Caginalp phase-field system with dynamic boundary conditions and singular potentials"http://hdl.handle.net/11380/612438Titolo: Corrigendum to"Existence of global solutions to the Caginalp phase-field system with dynamic boundary conditions and singular potentials"
Abstract: We correct the proof of Theorem 2.3 of the previous paper, assuming in advance a suitable growth of the potential approaching the singularities.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11380/6124382008-01-01T00:00:00ZTrajectory and global attractors for evolution equations with memoryhttp://hdl.handle.net/11380/453669Titolo: Trajectory and global attractors for evolution equations with memory
Abstract: Our aim in this note is to analyze the relation between two notionsof attractors for the study of the long time behavior of equationswith memory, namely, the global attractor in the so-called pasthistory approach, and the more recently proposed notion of trajectory attractor.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11380/4536692006-01-01T00:00:00ZRobust family of exponential attractors for isotropic crystal modelshttp://hdl.handle.net/11380/1100725Titolo: Robust family of exponential attractors for isotropic crystal models
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11380/11007252016-01-01T00:00:00ZLong time behavior of the Caginalp system with singular potentials and dynamic boundary conditionshttp://hdl.handle.net/11380/671645Titolo: Long time behavior of the Caginalp system with singular potentials and dynamic boundary conditions
Abstract: This paper is devoted to the study of the well-posedness and the long time behavior of the Caginalpphase-field model with singular potentials and dynamic boundary conditions.Thanks to a suitable definition of solutions, coinciding with the strong ones underproper assumptions on the bulk and surfacepotentials, we are able to get dissipative estimates, leading tothe existence of the global attractor with finite fractal dimension,as well as of an exponential attractor.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11380/6716452012-01-01T00:00:00ZConvergence to stationary states of solutions to the semilinear equation of viscoelasticityhttp://hdl.handle.net/11380/461846Titolo: Convergence to stationary states of solutions to the semilinear equation of viscoelasticity
Abstract: We consider the equation of viscoelasticity characterized by a nonlinear elastic force φ depending on the displacement u and subject to a time dependent external load F. The dissipativity of the corresponding evolution system is only due to the presence of the relaxation kernel k. Rescaling k(s)-k(∞) with a relaxation time ε>0, we can find a sufficiently small ε_0>0, such that, if φ is real analytic and ε∈ (0,ε_0], then any sufficiently smooth u converges to a single stationary state with an algebraic decay rate, provided that F suitably converges to a time independent load.The proof relies on the well-known Łojasiewicz-Simon inequality.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11380/4618462006-01-01T00:00:00ZAsymptotic behavior of a phase-field system with dynamic boundary conditionshttp://hdl.handle.net/11380/461845Titolo: Asymptotic behavior of a phase-field system with dynamic boundary conditions
Abstract: This article is devoted to the study of the asymptotic behavior of aCaginalp phase-field system with nonlinear dynamic boundary conditions. As a proper parameter ε goes to zero, this problem converges to the viscous Cahn-Hilliard equation. We firstprove the existence and uniqueness of the solution to the system and then provide an upper semicontinuous family of globalattractors A_ε . Furthermore, we prove the existence of anexponential attractor for each problem, which yields, since it contains the aforementioned global attractor, the finite fractal dimensionality of A_ε.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11380/4618452006-01-01T00:00:00Z