Patrick GuidottiAssociate Professor, Mathematics |
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Research Interests |
Nonlinear Partial Differential Equations and their Applications | |
| URL | math.uci.edu/~gpatrick/ | |
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Academic Distinctions |
Auszeichung (distinction) for Ph.D. Thesis. First prize of the Preisinstitut of the Universität Zürich for an outstanding dissertation. Supported Fellow of the Schweizerische Studienstiftung from 1992-1996. Research Fellowship of the Swiss National Science Foundation. |
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| Appointments |
1999-2001: Von Karman Instructor, Applied Mathematics, California Institute of Technology. 1997-1999: Postdoctoral Scholar in the Swiss National Science Foundation Fellowship. |
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Research Abstract |
My research focuses on nonlinear Partial Differential Equations, in particular of elliptic and parabolic type and their applications. I am interested in well-posedness, regularity and global existence of solutions and their qualitative properties as well as some aspects of their numerical resolution. | |
| Publications | (With J. Lambers) "Eigenvalue Characterization and Computation for the Laplacian on general 2D domains". To appear in Numerical Functional Analysis and Optimization. | |
| (With J. Lambers) “Two New Nonlinear Nonlocal Diffusions for Noise Reduction”, to appear in Journal of Mathematical Imaging and Vision. | ||
| "Numerical Approximation of Generalized Functions: Aliasing, the Gibbs Phenomenon and a Numerical Uncertainty Principle", Functional Analysis and Evolution Equations, pp. 331-356, Birkhaeuser, Basel (2008). | ||
| “A globally well-posed nonlinear nonlocal diffusion”, Proceedings of ICIAM 2007, Zurich. | ||
| “Singular Elliptic and Parabolic Problems and a Class of Free Boundary Problems”, Proceedings of ICIAM 2007, Zurich. | ||
| "Optimal Regularity for a Class Singular Cauchy Problems", Journal of Differential Equations, Vol. 232, No. 2, pp 468-486 (2007). | ||
| "A Class of Free Boundary Problems with Onset of a new Phase", SIAM J. on Math. Anal., Vol. 36, No. 6, pp. 1981-2004 (2007). | ||
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(with J. Lambers and K. Solna) "1D Analysis of Wave Propagation in inhomogeneous media". Numerical Functional Analysis and Optimization, Vol. 27 (1) 2006, 25-55. |
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| "Generalized Fundamental Solutions ", Abstract and Applied Analysis no. 1 2005, 45-57. | ||
| "Elliptic and parabolic problems in unbounded domains". Mathematische Nachrichten, 272 (2004), pp. 32-44. | ||
| "A new first-kind boundary integral formulation for the the Laplace Dirichlet-to-Neumann map in 2D". Journal of Computational Physics 190 (2003), pp. 325-345. | ||
| "Problems in Unbounded Cylindrical Domains". Proceedings of the conference "Elliptic and Parabolic Problems: Recent Advances", NTHU, Taiwan (2003). | ||
| (With R. Pajarola and M. Sainz) "Object-Space Blending and Splatting". Sketches & Applications Catalog SIGGRAPH 2003. ACM, 2003. | ||
| "A 2D free boundary value problem and singular elliptic boundary value problems". Journal of Evolution Equations, Vol. 2 (4), 395--424 (2002). | ||
| (with D. Bernstein) "Modeling and analysis of hysteresis phenomena in electrostatic zipper actuators". Proceedings of Modeling and Simulation of Microsystems 2001, Hilton Head Island, SC, pp 306-309. | ||
| (with D. Bernstein and J. A. Pelesko) "Analytical and numerical analysis of electrostatically actuated MEMS devices". Proceedings of Modeling and Simulation of Microsystems 2000, San Diego, CA, pp 489-492. | ||
| (with S. Merino) "Gradual loss of positivity and hidden invariant cones in a scalar heat equation". Differential and integral equations, Vol.13 (10-12) (2000), pp 1551-1568. | ||
| "Diffusion in glassy polymers: sorption of a finite amount of swelling solvent". NoDEA 6 (1999), pp 297-317. | ||
| "Singular quasilinear abstract cauchy problems". Nonlinear Analysis TMA 32(5) (1998), pp 667-695. | ||
| (with J. Pelesko) "Transient instability in Case II diffusion". Journal of Polymer Science: Part B: Polymer Physics, Vol.36 (1998), pp 2941-2947. | ||
| "Diffusion in glassy polymers: a free boundary value problem". Advances in Mathematical Sciences and Applications, 7(2) (1997), pp 675-693. | ||
| (with S. Merino) "Hopf bifurcation in a scalar reaction diffusion equation". Journal of Differential Equations, 140 (1) (1997), pp 209-222. | ||
| Grants | NSF-CMS-0330470 (Co-Pi, 2003-2006) "Sensors: Broad-Bandwidth High-Resolution MEMS Array of Inertial Sensors with Embedded Optical Detection'' | |
| NSF-DMS-0712875 (single PI, 2007-2010) “Nonlinear Diffusions and Image Processing” | ||
| Link to this profile | http://www.faculty.uci.edu/profile.cfm?faculty_id=4830 | |
| Last updated | 08/15/2008 | |