1,721,266 research outputs found
Inverse and direct problems for nonautonomous degenerate integrodifferential equations of parabolic type with Dirichlet boundary conditions
No full textThis paper deals with inverse and direct problems related to linear degenerate integrodifferential equations of parabolic type. The study of the direct problem is highly affected by the related inverse problems so that the results of the direct problems are just those needed to solve – locally in time – the inverse one. The latter is concerned with recovering – in a Hölder class – a memory kernel depending on time only
Degenerate integrodifferential equations of parabolic type
No full textIl contributo è un articolo scientifico originale, non pubblicato altrove in nessuna forma, e sottoposto a referee. Il volume contiene solo articoli originali.We consider the initial value problem for a possibly degenerate in-tegrodifferential equation in L2(Ω) (eqution found) where M(t) = M0M1(t) is the multiplication operator by the function m(x, t) = m0(x)m1(x, t), m0(x) ≥ 0, m1(x, t) ≥ c > 0, L(t) is the realization in L2(Ω) of a second-order strongly elliptic operator in divergence form with Dirichlet or Neumann boundary conditions for all t, and B(t, s) is a linear differential operator of order ≤ 2 for each (t, s), 0 ≤ s ≤ t ≤ T, Ω being a bounded open set in Rn with a smooth boundary. We also establish a corresponding result in Lp(Ω), 1 < p < 3/2, related to Dirichlet boundary condition, only
Some identification problems related to thermal materials with loss of memory
No full textIl contributo è un articolo scientifico originale, non pubblicato altrove in nessuna forma.
The author considers a new class of identification problems for integro-differential parabolic equations describing the evolution of the temperature in a material with memory. The memory effects are taken into account by convolution kernels that are in general unknown. There is a large body of literature for identification problems consisting in determining both the temperature and the convolution memory kernel with the assumption that additional measurements on the temperature are taken into account. The new problem the author considers is the determination of a suitable additional function (together with the temperature and the convolution memory kernel) that appears in one of the extremes of integration, that is, in the convolution integral of the evolution equation of the temperature. This term takes into account the loss of memory of the material. In the references of the paper we find the motivation for the study of such new problems
Architetture costruite per resistere/Architectures built to endure
No full textL’opera di Paulo David, David, nato a Funchal, sull’isola portoghese di Madeira nel 1959, è professore ordinario, presso il Dipartimento ABC del Politecnico, ha ottenuto, ormai da molti anni, un ampio riconoscimento internazionale, attestato da pubblicazioni e premi tra cui l’Alvar Aalto Medal, (2012), uno dei più importanti riconoscimenti nel campo dell’architettura. Continua tuttavia a rimanere, come la sua ricerca, non scontata, rara e singolare nel panorama attuale dell’architettura, non appariscente, ma silenziosa e appartata. Il legame di Paulo David con il Politecnico è iniziato quasi una decina di anni fa, al Polo territoriale di Mantova, dove è arrivato per la prima volta nel 2016. Eduardo Souto de Moura dava inizio alla sua attività di professore del Politecnico, fortemente voluto da Federico Bucci, e aveva riunito a supportarlo alcuni più giovani architetti portoghesi tra cui appunto Paulo David.Paulo David’s work has been internationally recognised for many years now, as evidenced by publications and awards such as the Alvar Aalto Medal (2012), one of the most important prizes in the field of architecture. But his work continues to be surprising, rare and unique in the panorama of contemporary architecture, not ostentatious, but quiet and detached. Paulo David’s relationship with the Politecnico began almost a decade ago, at the Mantua campus, where he first arrived in 2016. Eduardo Souto de Moura was beginning his work as a professor at the Politecnico, strongly promoted by Federico Bucci, and had gathered a few younger Portuguese architects to support him, including Paulo Davi
Exponential attractors for semiconductor equations
No full textThis paper studies the asymptotic behaviour of solutions to the classical semiconductor equations due to Shockley. We will construct not only global solutions but also exponential attractors for the dynamical system determined from the Cauchy problem. Exponential attractors — such a notion was introduced by Eden, Foias, Nicolaenko and Temam — are positively invariant sets which contain the global attractor, have finite fractal dimensions and attract every trajectory in an exponential rate
Direct and inverse problems for second-order integro-differential operator equations subject to non-initial conditions
No full textAn identification problem for a conserved phase-field model with memory
No full textThis paper is devoted to recovering a scalar memory kernel in a conserved phase-field model. For such a problem local in time existence and uniqueness results are proved. The technique used allows to show also the continuous dependence on the kernel of the solution to the direct problem
Identification problems in Banach spaces for linear first-order partial differential equations in one space dimension and applications
No full textWe prove existence and uniqueness results for mild solutions to direct and inverse Cauchy problems related to linear first-order partial differential equations in Banach spaces. Some applications are given to ultraparabolic differential and integrodifferential problems
A degenerate parabolic identification problem: the Hilbertian case
No full textWe recover a non-negative time-dependent function, vanishing only at t = 0, in a linear multi-dimensional parabolic equation with a non-integrable degeneration concentrated at t = 0. First we prove a global in time existence and uniqueness result for the direct problem in a general Hilbert space, via Fourier representation of the solution to the direct problem. Then we show a similar result, but local in time only, for the identification problem. Finally, we apply such a result to our specific linear parabolic equation related to a smooth bounded domain in Rd, d = 1, 2, 3
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