Publications and Work in Progress

P. Guidotti, S. Merino, "On Wiener's Violent Oscillations, Popov's curves and Hopf's Supercritical Bifurcation for a Scalar Heat Equation"
Preprint.

P. Guidotti, S. Merino, "On the Maximal Parameter Range of Global Stability for a Nonlocal Thermostat Model"
Preprint to appear in Journal of Evolution Equations.

D. Agress, P. Guidotti, D. Yan, "The Smooth Extension Embedding Method with Chebyshev Polynomials"
Preprint.

D. Agress, P. Guidotti, "The Smooth Extension Embedding Method",
Preprint to appear in SIAM Journal of Scientific Computing.

P. Guidotti, "Using an Encompassing Periodic Box to Perform Numerical Calculations on General Domains",
Journal of Elliptic and Parabolic Equations 6 (1), 2020.

T. Ma, K. E. Wood, D. Xu, P. Guidotti, A. Pantano, N. L. Komarova, "Admission predictors for success in a mathematics graduate program",
Preprint and Letter in the Notices of the AMS.

P. Guidotti, C. Walker, "On a model for a sliding droplet: Well-posedness and stability of translating circular solutions",
Journal of Mathematical Analysis and Applications 50 (2), 2018.

O. Bruno, P. Guidotti, M.B. Neiva, "Improving LBP and its variants using anisotropic diffusion"
International Journal of Modern Physics C 29 (8), 2018.

P. Guidotti, "Domain Variations for Moving Boundary Problems",
Calculus of Variations and PDEs 56 (3), 2017.

P. Guidotti and Y. Shao, "Wellposedness of a nonlocal nonlinear diffusion equation of image processing",
Nonlinear Analysis 150 (2017).

P. Guidotti, "A Class Of Elliptic Equations with Interior Degeneration",
Journal of Mathematical Imaging and Vision 58 (3), 2017.

P. Guidotti, "Equilibria and Their Stability for a droplet model",
Nonlinearity 28 (2015).

G.A. Wirth, D.S. Mowlds, P. Guidotti, A. Salibian, A. Nguyen, K. Paydar, "A cellular dermal matrix fenestration and their effect on breast shape: a mathematical model as proof of concept",
European Journal of Plastic Surgery 38 (4), 2015.

J. Escher, P. Guidotti, "Local Well-posedness for a quasi-stationary droplet model",
Calculus of Variations and PDEs, Vol. 54 (1) 2015.

P. Guidotti, "Anisotropic Diffusions of Image Processing From Perona-Malik on",
Adv. Stud. Pure Math. 67, Math. Soc. Japan, Tokyo, 2015.

J. Escher, P. Guidotti, C. Walker, "Two-Phase Flow in Rotating Hele-Shaw Cells with Coriolis Effects".
Interfaces and Free Boundaries, Vol. 15 (2) 2013.

P. Guidotti, Y. Kim, and J. Lambers, "Image restoration with a new class of forward-backward-forward diffusion equations of Perona-Malik type with Applications to Satellite Image Enhancement".
SIAM Journal on Imaging Science, Vol. 6 (3) 2013.

P. Guidotti, "A backward-forward regularization of the Perona-Malik equation".
Journal of Differential Equations, Vol. 252 (4) 2012.

P. Guidotti, "A family of nonlinear diffusions connecting Perona-Malik to standard diffusion".
Discrete and Continuous Dynamical Systems - Series S, Vol. 5 (3) 2012.

P. Guidotti, K. Longo, "Two Enhanced Fourth Order Diffusion Models for Image Denoising".
Journal of Mathematical Imaging and Vision, Vol. 40 2011, 188-198.

P. Guidotti, K. Longo, "Well-posedness for a Class of Fourth Order Diffusions of Image Processing".
NoDEA Nonlinear Differential Equations Appl., Vol. 18 (4) 2011, 407-425.

M. Webster, P. Guidotti, "Nonlinear Stability Analysis of a Two-Dimensional Diffusive Free Boundary Problem".
Interfaces and Free Boundaries, Vol. 12 (3) 2010, 293-310.

P. Guidotti, "A New Well-posed Nonlinear Nonlocal Diffusion for Noise Reduction".
Nonlinear Analysis: Theory, Methods, and Applications, Vol. 72 (12) 2010, 4625-4637.

M. Webster, P. Guidotti, "Boundary Dynamics of a two-dimensional diffusive free boundary problem".
Discrete and Continuous Dynamical Systems - Series A, Vol. 26 (2) 2010, 713-736.

P. Guidotti, "Some Anisotropic Diffusions".
Ulmer Seminare, Heft 14, 2009, 215-221.

P. Guidotti, "A New Nonlocal Nonlinear Diffusion of Image Processing".
Journal of Differential Equations, Vol. 246 (12), 2009, 4731-4742.

P. Guidotti, J. Lambers, "Two New Nonlinear Nonlocal Diffusions for Noise Reduction".
Journal of Mathematical Imaging and Vision, Vol. 33 (1) 2009, 25-37.

P. Guidotti, J. Lambers, "Eigenvalue Characterization and Computation for the Laplacian on general 2D domains", Numerical Functional Analysis and Optimization Vol. 29 (5-6) 2008, 507-531.

P. Guidotti, "Numerical Approximation of Generalized Functions: Aliasing, the Gibbs Phenomenon and a Numerical Uncertainty Principle", Functional Analysis and Evolution Equations: Dedicated to Günther Lumer, Birkhäuser Basel 2008, 331-356.

P. Guidotti, A Class of Free Boundary Problems with Onset of a new Phase.
SIAM J. on Math. Anal. Vol. 38 (6) 2007, 1981-2004.

P. Guidotti, Optimal Regularity for a Class Singular Cauchy Problems.
Journal of Differential Equations Vol. 232 (2) 2007 468-486.

P. Guidotti, J. Lambers, K. Solna, "1D Analysis of Wave Propagation in inhomogeneous media".
Numerical Functional Analysis and Optimization, Vol. 27 (1) 2006, 25-55.

P. Guidotti, "Semiclassical Fundamental Solutions", Abstract and Applied Analysis, no. 1 2005, 45-57

R. Pajarola, M. Sainz, P. Guidotti, "Confetti: Object-Space Point Blending and Splatting", IEEE Transactions on Visualization and Computer Graphics, Vol. 10 (5) 2004, 598-608.

P. Guidotti, "Elliptic and Parabolic Problems in Unbounded Domains", Mathematische Nachrichten, 272 (2004), pp. 32-44.

R. Pajarola, M. Sainz, P. Guidotti, "Object-Space Blending and Splatting", Sketches & Applications Catalog SIGGRAPH 2003. ACM, 2003

P. Guidotti, "Problems in Unbounded Cylindrical Domains", Proceedings of the conference "Elliptic and Parabolic Problems: Recent Advances", NTHU, Taiwan (2003).

P. Guidotti, "A new first-kind boundary integral formulation for the the Laplace Dirichlet-to-Neumann map in 2D", Journal of Computational Physics 190 2003, 325-345.

P. Guidotti, "2-D Free Boundary Value Problem with Onset of a Phase and Singular Elliptic Boundary Value Problems", Journal of Evolution Equations, Vol. 2 (4) 2002, 395-424.

P. Guidotti, D. Bernstein, "Modeling and Analysis of Hysteresis Phenomena in Electrostatic Zipper Actuators", Proceedings of Modeling and Simulation of Microsystems 2001, Hilton Head Island, SC, 306-309.

D. Bernstein, P. Guidotti, J. Pelesko, "Analytical and Numerical Analysis of Electrostatically Actuated MEMS Devices", Proceedings of Modeling and Simulation of Microsystems 2000, San Diego, CA, 489-492.

P. Guidotti, 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. [DVI][PS]

P. Guidotti, "Diffusion in glassy polymers: Sorption of a finite amount of swelling solvent", Nonlinear Differential Equations and Applications 6 (3) 1999, 297-317.

P. Guidotti, J. Pelesko, "Transient Instability in Case II Diffusion", Journal of Polymer Science, Part B: Polymer Physics, Vol. 36 (16) 1998, 2941-2947 (1998)

P. Guidotti, "Singular Quasilinear Abstract Cauchy Problems", Nonlinear Analysis TMA 32 (5) 1998, 667-695.

P. Guidotti, S. Merino, "Hopf Bifurcation in a Scalar Reaction Diffusion Equation", Journal of Differential Equations 140 (1) 1997, 209-222.

P. Guidotti, "Diffusion in glassy polymers: A free boundary value problem", Advances in Mathematical Sciences and Applications 7 (2) 1997, 675-693 (1997). [DVI][PS]

P. Guidotti, M. Hieber, "An integral equation arising in the study of above threshold photodetachment", Helvetica Physica Acta 68 (7-8) 1995, 627-634. [DVI][PS]

Noisy
   boat Boat1
Boat2 Boat3
Original boat Method noise