Università degli Studi di PadovaDipartimento di Matematica ''Tullio Levi-Civita''Home Page di Claudio Marchi |
[Indirizzo | Didattica | Pubblicazioni]
Claudio Marchi
Professore associato di Analisi Matematica MAT/05
Università degli Studi di Padova
Dipartimento di Matematica "Tullio Levi-Civita"
via Trieste 63,
35121 Padova (Italy)
studio 5DA3
telefono: +39-0498271498
E-mail: marchi"at"math.unipd.it
[Analisi Matematica 1 | Introduction to Partial Differential Equations ]
| Docente: | Claudio Marchi. |
| Studenti: | afferiscono a questo canale gli studenti la cui matricola finisce con i numeri 5,6,7,8 o 9. |
| Docenti altri canali: | Bruno Bianchini, Valentina Franceschi, Elio Marconi, Monica Motta, Franco Rampazzo. |
| Orario: | Lu-Ve 16:30 - 18:30, Ma-Me 8:30 - 10:30. Aula 0E del Complesso Vallisneri. |
| Testi di riferimento: | Marson, Baiti, Ancona, Rubino: "Analisi Matematica 1, teoria ed applicazioni", Carocci (2010). |
| Bramanti, Pagani, Salsa: "Analisi Matematica 1", Zanichelli (2008). | |
| Languasco: "Analisi Matematica 1", Hoepli (2017). | |
| Precorso di calcolo: | precorso di calcolo online tenuto da docenti del Dipartimento di Matematica. |
| Programma svolto: | Programma aggiornato e dettagliato degli argomenti svolti a lezione. |
| Elearning: | Su Elearning sono disponibili gli appunti di lezione ed altre informazioni relative al corso. Iscrivetevici! |
| Date degli appelli: | Si consiglia di controllare questa pagina web o quella di Elearning relativa a questo corso. |
| Orientativamente saranno: | |
| Primo appello. Scritto: lunedì 22 gennaio 2024. Temi. Temi svolti. Orale: venerdì 26 gennaio (con possibile prosieguo al 28 e/o 30). |
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| Secondo appello. Scritto: lunedì 12 febbraio. Temi. Temi svolti. Orale: venerdì 16 febbraio (con possibile prosieguo al 18 e/0 20). | |
| Terzo appello. | |
|
Scritto: lunedì 1 luglio.
Orale: venerdì 5 luglio. |
|
| Quarto appello. | |
| Scritto: lunedì 9 settembre.
Orale: venerdì 13 settembre. |
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| Modalità di esame: | Consultare le informazioni di carattere generale (obiettivi, prerequisiti, regole d'esame). |
| Tutor: | Sono previste attività telematiche di studio organizzato con tutor junior. Orario: mercoledì alle 10:30 in aula 0E (da confermare). |
| Altre informazioni: | Nella pagina contenente tutte le informazioni si possono trovare anche i risultati di apprendimento previsti, un programma indicativo, ulteriori testi di consultazione, le modalità di esame in dettaglio, link a pagine utili. |
| Teachers: | Claudio Marchi and Fabio Paronetto. |
| Students: | students of Mathematics and students freely enrolled. |
| Timetable: | Monday and Tuesday 10:30 - 12:30, room 1BC50, Torre Archimede. |
| Recommended books: | S. Salsa and G. Verzini: "Partial Differential Equations in Action - From modelling to theory". |
| C. Evans: "Partial differential equations". | |
| E. Di Benedetto: "Partial differential equations". | |
| Elearning: | The notes of the lessons and any other information are available in Elearning. |
| Examination methods: | The exam consists in an oral examination. | Exam sessions: |
| First session: January 25th, 2024. | |
| Second session: February 7th, 2024. | |
| Third session: July 11th, 2024. | |
| Fourth session: September 12th, 2024. | |
| Fifth session: September 26th, 2024. | |
| Other informations: | see educational offer site. |
Y. Achdou, P. Mannucci, C. Marchi and N.A. Tchou: " First order Mean Field Games on networks", arXiv:2207.10908.
P. Mannucci, C. Marchi and N.A. Tchou: "First order Mean Field Games in the Heisenberg group: periodic and non periodic case", arXiv:2010.09279.
38. F. Camilli and C. Marchi: "On quasi-stationary mean field games of controls", Appl. Math. Optim. 87 (2023), no. 3, Paper No. 47.
37. D. Ghilli and C. Marchi: "Rate of convergence for singular perturbations of Hamilton-Jacobi equations in unbounded spaces", J. Math. Anal. Appl. 526 (2023), no. 1, Paper No. 127225.
36. Y. Achdou, P. Mannucci, C. Marchi and N.A. Tchou: "Deterministic mean field games with control on the acceleration and state constraints", SIAM J. Math. Anal. 54 (2022), n.3, 3757-3788.
35. F. Camilli and C. Marchi: "A note on Kazdan-Warner equation on networks", Adv. Calc. Var. 15 (2022), n. 4, 693-704.
34. P. Mannucci, C. Marchi and N.A. Tchou: "Non coercive unbounded first order mean field games: the Heisenberg example", J. Differential Equations 309 (2022), 809–840.
33. Y. Achdou, P. Mannucci, C. Marchi and N.A. Tchou: "Deterministic mean field games with control on the acceleration", NoDEA Nonlinear Differential Equations Appl. 27 (2020), no. 3, Paper No. 33, 32 pp.
32. P. Mannucci, C. Marchi, C. Mariconda and N.A. Tchou: "Non-coercive first order Mean Field Games", J. Differential Equations 269 (2020), no. 5, 4503--4543.
31. N. Dirr, F. Dragoni, P. Mannucci and C. Marchi: "$\Gamma$-convergence and homogenisation for a class of degenerate functionals", Nonlinear Anal. 190 (2020), 111618, 25pp..
30. P. Mannucci, C. Marchi and N.A. Tchou: "Asymptotic behaviour for operators of Grushin type: invariant measure and singular perturbations", Discrete Contin. Dyn. Syst. Ser. S 12 (2019), n. 1, 119-128.
29. S. Cacace, F. Camilli, A. Cesaroni and C. Marchi: "An ergodic problem for Mean Field Games: qualitative properties and numerical simulations", Minimax Theory Appl. 3 (2018), n. 2, 211-226.
28. N. Dirr, F. Dragoni, P. Mannucci and C. Marchi: "Stochastic homogenization for functionals with anisotropic rescaling and non-coercive Hamilton-Jacobi equations", SIAM J. Math. Anal. 50 (2018), n. 5, 5198-5242.
27. P. Mannucci, C. Marchi and N.A. Tchou: "Singular perturbations for a subelliptic operator", ESAIM Control Optim. Calc. Var. 24 (2018), n. 4, 1429-1451.
26. F. Camilli, E. Carlini and C. Marchi: "A flame propagation model on a network with application to a blocking problem", Discrete Contin. Dyn. Syst. Ser. S 11 (2018), n. 5, 825-843.
25. S. Cacace, F. Camilli and C. Marchi: "A numerical method for Mean Field Games on networks", ESAIM Math. Model. Numer. Anal. 51 (2017), no. 1, 63-88.
24. A. Cesaroni, N. Dirr and C. Marchi: "Homogenization of a mean field game system in the small noise limit", SIAM J. Math. Anal. 48 (2016), no. 4, 2701-2729.
23. P. Mannucci, C. Marchi and N. Tchou: "The ergodic problem for some subelliptic operators with unbounded coefficients", NoDEA Nonlinear Differential Equations Appl. vol. 23 (2016), no. 4, Art. 47, 26 pages.
22. F. Camilli and C. Marchi: "Stationary Mean Field Games systems defined on networks", SIAM J. Control Optim. 54 (2016), no. 2, 1085-1103.
21. F. Camilli, R. Capitanelli and C. Marchi: "Eikonal equations on the Sierpinski gasket", Math. Ann. 364 (2016), no. 3-4, 1167-1188.
20. F. Camilli, E. Carlini and C. Marchi: "A model problem for Mean Field Games on networks", Discrete Contin. Dyn. Syst. 35 (2015), no.9, 4173-4192.
19. C. Marchi: "Continuous dependence estimates for the ergodic problem of Bellman equation with an application to the rate of convergence for the homogenization problem", Calc. Var. Partial Differential Equations 51 (2014), no.3-4, 539-553.
18. F. Camilli and C. Marchi: "A comparison among various notions of viscosity solutions for Hamilton-Jacobi equations on networks", J. Math. Anal. Appl. 407 (2013), no. 1, 112-118.
16. F. Camilli, C. Marchi and D. Schieborn: "The vanishing viscosity limit for Hamilton-Jacobi equations on networks", J. Differential Equations 254 (2013), no. 10, 4122-4143.
17. F. Camilli, D. Schieborn and C. Marchi: "Eikonal equations on ramified spaces", Interfaces Free Bound. 15 (2013), no. 1, 121-140.
15. C. Marchi: "Continuous dependence estimates for the ergodic problem of Bellman-Isaacs operators via the parabolic Cauchy problem", ESAIM Control Optim. Calc. Var.18 (2012), no. 4, 954-968.
14. F. Camilli and C. Marchi: "Continuous dependence estimates and homogenization of quasi-monotone systems of fully nonlinear second order parabolic equations", Nonlinear Anal. 75 (2012), no. 13, 5103-5118.
13. F. Camilli, A. Cesaroni and C. Marchi: "Homogenization and vanishing viscosity in fully nonlinear elliptic equations: rate of convergence estimates", Adv. Nonlinear Stud. 11 (2011), no. 2, 405-428.
12. F. Camilli and C. Marchi: "On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems", Netw. Heterog. Media 6 (2011), no. 1, 61-75.
11. C. Marchi: "On the rate of convergence of singular perturbations of Hamilton-Jacobi equations", Comm. Pure Appl. Anal. 9 (2010), no. 5, 1363-1377.
10. F. Camilli and C. Marchi: "Rates of convergence in periodic homogenization of fully nonlinear uniformly elliptic PDEs", Nonlinearity 22 (2009), no. 6, 1481-1498.
9. C. Marchi: "Rate of convergence for multiscale homogenization of Hamilton-Jacobi equations", Proc. Roy. Soc. Edinburgh Sect. A 139 (2009), no. 3, 519-539.
8. O. Alvarez, M. Bardi and C. Marchi: "Multiscale singular perturbation and homogenization of optimal control problems", in Geometric control and nonsmooth analysis (Eds.: F. Ancona, A. Bressan, P. Cannarsa, F. Clarke and P. Wolenski), Series on Advances in Mathematics for Applied Sciences no. 76, World Scientific (2008), 1-27.
7. O. Alvarez, M. Bardi and C. Marchi: "Multiscale problems and homogenization for second-order Hamilton-Jacobi equations", J. Differential Equations 243 (2007), no. 2, 349-387.
6. P. Cardaliaguet and C. Marchi: "Regularity of the Eikonal Equation with Neumann Boundary Conditions in the Plane: Application to Fronts with Nonlocal Terms", SIAM J. Control Optim. 45 (2006), no. 3, 1017-1038.
5. C. Marchi: "Homogenization for fully nonlinear parabolic equations", Nonlinear Anal. 60 (2005), no. 3, 411-428.
4. C. Marchi: "Well-posedness for parabolic equations of arbitrary order", Asymptot. Anal. 35 (2003), no. 1, 41-64.
3. C. Marchi: "Averaging for non-periodic fully nonlinear equations", Electron. J. Differential Equations 2003, no. 95, (electronic).
2. C. Marchi: "The Cauchy problem for the heat equation with a singular potential", Differential Integral Equations 16 (2003), no. 9, 1065-1081.
1. C. Marchi and A. Tesei: "Higher-order parabolic equations without conditions at infinity", J. Math. Anal. Appl. 269 (2002), no. 1, 352-368.