1,720,999 research outputs found
Temi d’esame di Analisi Matematica I. Vol. 1, Numeri complessi, numeri reali, successioni, serie ed integrali
No full textI due volumi di esercizi di cui questo è il primo, raccolgono temi d’esame svolti dei corsi di Analisi Matematica 1 (precedentemente denominati Matematica 1) tenuti presso la facoltà di Ingegneria dell’Università di Bergamo negli anni 2004-2012. Tutti gli esercizi presentati sono completamente e dettagliatamente svolti. Gli argomenti trattati nel Volume 1 sono numeri complessi, numeri reali (in particolare ricerca di massimo, minimo, estremo superiore ed estremo inferiore di insiemi numerici), successioni, serie ed integrali, definiti, indefiniti e generalizzati
Strichartz inequalities for the Schrödinger equation with the full Laplacian on the Heisenberg group
No full textWe prove Strichartz inequalities for the solution of the Schrödinger equation related to the full Laplacian on the Heisenberg group. A key point consists in estimating the decay in time of the L∞ norm of the free solution; this requires a careful analysis due also to the non-homogeneous nature of the full Laplacian
Sur l'unicité dans L3R3 des solutions « mild » des équations de Navier-Stokes
No full textWe prove uniqueness in L3(R3) for mild solutions of the Navier-Stokes equations when the initial data are small enough. The proof lies on an estimate in the Ḃ1/2∞2(R3) norm for the bilinear term.Nous prouvons l'unicité dans L31253-2 des solutions « milddes équations de Navier-Stokes lorsque la donnée initiale est de taille suffisamment petite. La démonstration repose sur l'estimation du terme bilinéaire dans l'espace Ḃ1/2∞2(R3)
Temi d'esame di Analisi Matematica I. Vol. 2, Limiti e studio di funzione
No full textI due volumi di esercizi di cui questo è il secondo, raccolgono temi d’esame svolti dei corsi di Analisi Matematica 1 (precedentemente denominati Matematica 1) tenuti pres- so la facoltà di Ingegneria dell’Università di Bergamo negli anni 2004-2012. Tutti gli esercizi presentati sono completamente e dettagliatamente svolti. Gli argomenti trattati nel Volume 2 sono limiti e studio di funzione reale di una variabile reale. In particolare, nel capitolo sullo studio di funzione, oltre ai classici studi del grafico di una funzione tramite le sue proprietà essenziali, sono presentati anche esercizi specifici sullo studio di continuità e derivabilità, sulla determinazione della retta tangente e sui polinomi di Taylor, oltre che sulla composizione e inversione di funzioni
Fokker-Planck equations and n-dimensional Poincaré inequalities for isotropic densities
Full text linkWe consider new connections between the problem of trend to equilibrium for the n-dimensional Fokker-Planck equation of statistical physics, and weighted Poincaré inequality. To this aim we consider a class of n-dimensional Fokker-Planck equations with variable isotropic coefficient of diffusion and drift, inspired by the analogous one-dimensional Fokker-Planck equation appearing when studying the evolution of wealth distribution
Besov spaces and unconditional well-posedness for the nonlinear Schrödinger equation in H^s(R^n)
No full textHeat equation with an exponential nonlinear boundary condition in the half space
No full textWe consider the initial-boundary value problem for the heat equation in the half space with an exponential nonlinear boundary condition. We prove the existence of global-in-time solutions under the smallness condition on the initial data in the Orlicz space expL*2(R^N_+). Furthermore, we derive decay estimates and the asymptotic behavior for small global-in-time solutions
Fokker-Planck equations in the modeling of socio-economic phenomena
No full textWe present and discuss various one-dimensional linear Fokker-Planck-Type equations that have been recently considered in connection with the study of interacting multi-Agent systems. In general, these Fokker-Planck equations describe the evolution in time of some probability density of the population of agents, typically the distribution of the personal wealth or of the personal opinion, and are mostly obtained by linear or bilinear kinetic models of Boltzmann type via some limit procedure. The main feature of these equations is the presence of variable diffusion, drift coefficients and boundaries, which introduce new challenging mathematical problems in the study of their long-Time behavior
Wright–Fisher–type equations for opinion formation, large time behavior and weighted logarithmic-Sobolev inequalities
Full text linkWe study the rate of convergence to equilibrium of the solution of a Fokker–Planck type equation introduced in [G. Toscani, Kinetic models of opinion formation Commun. Math. Sci., 4 (3) (2006)] to describe opinion formation in a multi-agent system. The main feature of this Fokker–Planck equation is the presence of a variable diffusion coefficient and boundaries, which introduce new challenging mathematical problems in the study of its long-time behavior
Unicité dans l3(R3) et d'autres espaces fonctionnels limites pour Navier-Stokes
No full textThe main result of this paper is the proof of uniqueness for mild solutions of the Navier-Stokes equations in L3(R3). This result is extended as well to some Morrey-Campanato spaces
- …
