... the Cardiac Electric Field at Micro-and Macroscopic Level 49 Donatella Donatelli and Pierange... more ... the Cardiac Electric Field at Micro-and Macroscopic Level 49 Donatella Donatelli and Pierangelo Marcati Singular Limits for Nonlinear Hyperbolic Systems 79 Giuseppe Da Prato Bounded Perturbations of Ornstein-Uhlenbeck Semigroups 97 Angela Favini, Alfredo Lorenzi and ...
We perform a rigorous analysis of the quasineutral limit for a hydrodynamical model of a viscous ... more We perform a rigorous analysis of the quasineutral limit for a hydrodynamical model of a viscous plasma represented by the Navier Stokes Poisson system in $3-D$. We show that as $\lambda\to 0$ the velocity field $u^{\lambda}$ strongly converges towards an incompressible velocity vector field $u$ and the density fluctuation $\rho^{\lambda}-1$ weakly converges to zero. In general the limit velocity field cannot be expected to satisfy the incompressible Navier Stokes equation, indeed the presence of high frequency oscillations strongly affects the quadratic nonlinearities and we have to take care of self interacting wave packets. We shall provide a detailed mathematical description of the convergence process by using microlocal defect measures and by developing an explicit correctors analysis. Moreover we will be able to identify an explicit pseudo parabolic pde satisfied by the leading correctors terms. Our results include all the previous results in literature, in particular we show ...
We present a generalization of the div-curl lemma to a Banach space framework which is not includ... more We present a generalization of the div-curl lemma to a Banach space framework which is not included in the almost existing generalizations. An example is shown where this generalization is needed.
The IMA Volumes in Mathematics and its Applications, 2011
Abstract. In this paper we consider the global existence of weak solutions to a class of Quantum ... more Abstract. In this paper we consider the global existence of weak solutions to a class of Quantum Hydrodynamics (QHD) systems with initial data, arbitrarily large in the energy norm. These type of models, initially proposed by Madelung [24], have been extensively used in Physics to ...
Theory, Numerics and Applications(In 2 Volumes), 2012
ABSTRACT We describe the main difficulties that arise in performing the quasineutral limit for th... more ABSTRACT We describe the main difficulties that arise in performing the quasineutral limit for the Navier Stokes Poisson system.
ABSTRACT We derive rigorously a set of boundary conditions for heterogenous devices using a descr... more ABSTRACT We derive rigorously a set of boundary conditions for heterogenous devices using a description via the quantum hydrodynamic system provided by the Madelung transformations. In particular, we show that the generalized enthalpy should be constant at the interface between classical and quantum domains. This condition provides a set of boundary conditions, which we use to prove the existence and the uniqueness of regular steady solutions of the quantum hydrodynamic system. Finally, we analyse the linear stability of the system supplied with our boundary conditions and we test numerically our model on a toy device.
In this paper we investigate the zero-relaxation limit of the following multi-D semilinear hyperb... more In this paper we investigate the zero-relaxation limit of the following multi-D semilinear hyperbolic system in pseudodifferential form: W_{t}(x,t) + (1/epsilon) A(x,D) W(x,t) = (1/epsilon^2) B(x,W(x,t)) + (1/epsilon) D(W(x,t)) + E(W(x,t)). We analyse the singular convergence, as epsilon tends to 0, in the case which leads to a limit system of parabolic type. The analysis is carried out by using
... the Cardiac Electric Field at Micro-and Macroscopic Level 49 Donatella Donatelli and Pierange... more ... the Cardiac Electric Field at Micro-and Macroscopic Level 49 Donatella Donatelli and Pierangelo Marcati Singular Limits for Nonlinear Hyperbolic Systems 79 Giuseppe Da Prato Bounded Perturbations of Ornstein-Uhlenbeck Semigroups 97 Angela Favini, Alfredo Lorenzi and ...
We perform a rigorous analysis of the quasineutral limit for a hydrodynamical model of a viscous ... more We perform a rigorous analysis of the quasineutral limit for a hydrodynamical model of a viscous plasma represented by the Navier Stokes Poisson system in $3-D$. We show that as $\lambda\to 0$ the velocity field $u^{\lambda}$ strongly converges towards an incompressible velocity vector field $u$ and the density fluctuation $\rho^{\lambda}-1$ weakly converges to zero. In general the limit velocity field cannot be expected to satisfy the incompressible Navier Stokes equation, indeed the presence of high frequency oscillations strongly affects the quadratic nonlinearities and we have to take care of self interacting wave packets. We shall provide a detailed mathematical description of the convergence process by using microlocal defect measures and by developing an explicit correctors analysis. Moreover we will be able to identify an explicit pseudo parabolic pde satisfied by the leading correctors terms. Our results include all the previous results in literature, in particular we show ...
We present a generalization of the div-curl lemma to a Banach space framework which is not includ... more We present a generalization of the div-curl lemma to a Banach space framework which is not included in the almost existing generalizations. An example is shown where this generalization is needed.
The IMA Volumes in Mathematics and its Applications, 2011
Abstract. In this paper we consider the global existence of weak solutions to a class of Quantum ... more Abstract. In this paper we consider the global existence of weak solutions to a class of Quantum Hydrodynamics (QHD) systems with initial data, arbitrarily large in the energy norm. These type of models, initially proposed by Madelung [24], have been extensively used in Physics to ...
Theory, Numerics and Applications(In 2 Volumes), 2012
ABSTRACT We describe the main difficulties that arise in performing the quasineutral limit for th... more ABSTRACT We describe the main difficulties that arise in performing the quasineutral limit for the Navier Stokes Poisson system.
ABSTRACT We derive rigorously a set of boundary conditions for heterogenous devices using a descr... more ABSTRACT We derive rigorously a set of boundary conditions for heterogenous devices using a description via the quantum hydrodynamic system provided by the Madelung transformations. In particular, we show that the generalized enthalpy should be constant at the interface between classical and quantum domains. This condition provides a set of boundary conditions, which we use to prove the existence and the uniqueness of regular steady solutions of the quantum hydrodynamic system. Finally, we analyse the linear stability of the system supplied with our boundary conditions and we test numerically our model on a toy device.
In this paper we investigate the zero-relaxation limit of the following multi-D semilinear hyperb... more In this paper we investigate the zero-relaxation limit of the following multi-D semilinear hyperbolic system in pseudodifferential form: W_{t}(x,t) + (1/epsilon) A(x,D) W(x,t) = (1/epsilon^2) B(x,W(x,t)) + (1/epsilon) D(W(x,t)) + E(W(x,t)). We analyse the singular convergence, as epsilon tends to 0, in the case which leads to a limit system of parabolic type. The analysis is carried out by using
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Papers by Pierangelo Marcati