1,721,011 research outputs found
Automatic control of the temperature in phase change problems with memory
No full textWe study a parabolic two-phase system with memory occupying a bounded and smooth domain. The heat exchange at part of the boundary is controlled by a thermostat. Assuming on the phase variable either a relaxation dynamics or a Stefan condition, we prove existence and uniqueness results for feedback control problems corresponding to two different types of thermostat: the relay switch and the Preisach operator. These results are strictly related to the continuous dependence of the solution on the boundary datum, which is investigated in advance
An existence result for an inverse problem for a quasilinear parabolic equation
No full textIn this paper we are concerned with a quasilinear parabolic equation with nonhomogeneous Cauchy and Neumann conditions arising in combustion theory: by the Schauder fixed point theorem, we give a local existence result for the solution to an inverse problem on a semi-infinite strand
Parabolic equation in theory of combustion: Direct and inverse problems
No full textIn questo lavoro, si riassumono i risultati ottenuti nella tesi di dottorato su un sistema parabolico semi-lineare in un dominio (cilindrico) non limitato con una condizione di Neumann nonlineare. Il modello proviene da studi sulla combustione nei propellenti solidi dei razzi. In letteratura era stata considerata solo l'approssimazione mono-dimensionale del modello: nella tesi, invece, si affrontano due problemi diretti sul modello 3-D e due problemi inversi su quello mono-dimensionale, arricchito dalla considerazione della presenza di reazioni chimiche sull'interfaccia solido-gas. Questi risultati sono contenuti in tre lavori pubblicati: i problemi diretti in una nota sui Rendiconti dell'Istituto Lombardo, Sezione A: Scienze Matematichee Applicazioni (1996) e i due problemi inversi su Inverse Problems (1998) e sul Journal of Inverse and Ill-posed problems.(1997
A stability result for an inverse problem related to a quasilinear parabolic equation
No full textWe study the stability of an unknown nonlinear term in a quasilinear parabolic equation arising in combustion theory. Choosing suitable spaces for data and nonlinear terms, we can show that the mapping data → nonlinear term is Hölder continuous
Singular limit of equations for linear viscoelastic fluids with periodic boundary conditions
No full textWe consider a one-parameter family of problems, governing, for any fixed parameter, the motion of a linear viscoelastic fluid in a two-dimensional domain with periodic boundary conditions. The asymptotic behavior of each problem is analyzed, by proving the existence of the global attractor. Moreover, letting the parameter go to zero, since the memory effect disappears, we obtain a limiting problem, given by the Navier–Stokes equations. For any fixed parameter, we construct an exponential attractor. The resulting family is robust, meaning that these exponential attractors converge, in an appropriate sense, to an exponential attractor of the limiting problem
Phase field systems with memory effects in the order parameter dynamics: convergence to standard phase field systems
No full textWe shall deal with two models arising in phase transition dynamics. The state of the system is described by the pair (θ,χ), where θ is the (relative) temperature and χ is the order parameter or phase field. The main difference between the two models relies on whether global constraints on χ are imposed or not: the resulting models will be called conserved or nonconserved, accordingly. Memory effects influencing both the heat flux and the dynamics of χ have been considered in a number of recent papers. Here we assume the Fourier law forthe heat flux in the energy balance equation, while we considermemory effects in the order parameter dynamics. We show thatsolutions to the phase field problems with memory converge to the solution to the standard phase field model, when the memorykernels suitably converge to the Dirac mass. This is done for boththe conserved and the nonconserved cases. Some error estimates are also obtained
Pullback exponential attractor for a Cahn-Hilliard-Navier-Stokes system in 2D
No full textWe consider a model for the evolution of a mixture of two incompressible and partially immiscible Newtonian fluids in two dimensional bounded domain. More precisely, we address the well-known model H consisting of the Navier-Stokes equation with non-autonomous external forcing term for the (average) fluid velocity, coupled with a convective Cahn-Hilliard equation with polynomial double-well potential describing the evolution of the relative density of atoms of one of the fluids. We study the long term behavior of solutions and prove that the system possesses a pullback exponential attractor. In particular the regularity estimates we obtain depend on the initial data only through fixed powers of their norms and these powers are independent of the growth of the polynomial potential considered in the Cahn-Hilliard equation
Robust family of exponential attractors for isotropic crystal models
No full textOur aim in this paper is to study, in term of finite dimensional exponential attractors, the Willmore regularization,
(depending on a small regularization parameter epsilon >0), of two phase-field equations, namely, the Allen–Cahn and the
Cahn–Hilliard equations. In both cases, we construct robust families of exponential attractors, that is, attractors that are
continuous with respect to the perturbation parameter
A one-dimensional wave equation with nonlinear damping
No full textWe consider a one-dimensional weakly damped wave equation, with a damping coefficient depending on the displacement. We prove the existence of a regular connected global attractor of finite fractal dimension for the associated dynamical system, as well as the existence of an exponential attractor
Well-posedness results for phase field systems with memory effects in the order parameter dynamics
No full textWe study two models arising in phase transition dynamics. Thestate of the system is described by the pair (θ,χ), where θ is the (relative) temperature and χ is the order parameter or phase field. The main difference between the two models relies on whether global constraints on χ are imposed or not: accordingly, the resulting models will be called conserved or nonconserved. Memory effects influencing both the heat flux and the dynamics of χ have been considered in a number of recent papers. Here we assume the Fourier law for the heat flux in the energy balance equation, while we consider memory effects in the order parameter dynamics. We analyze the well-posedness of corresponding Cauchy-Neumann problems for both conserved and nonconserved models. Various results are derived according to properties of the memory kernel involved
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