Research

Research projects

Joint publications with UT faculty and publications by post-doctoral or doctoral students.

  • Sílvia Barbeiro and Mary F. Wheeler: A-priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability.
  • I. N. Figueiredo, P. N. Figueiredo, G. Stadler, O. Ghattas and A. Araújo: Variational image segmentation for endoscopic human colonic aberrant crypt foci, IEEE Transactions on Medical Imaging.
  • I.N. Figueiredo, P.N. Figueiredo, N. Almeida, M.C. Leitão, O. Ghattas, G. Stadler: "Endoscopic Detection of Human Colonic Aberrant Crypt Foci using Mathematical Methods", Endoscopy 2008; 40 (Suppl 1) A 189.
  • D. Gomes, G. Terrone, “On the Bernstein estimate for systems of weakly coupled fully non-linear elliptic equations and integral operators”, to appear in CPAA.
  • D. Gomes, G. Terrone, "Aubry-Mather theory for discontinuous Lagrangians". submitted.
  • M. Bardi, G. Terrone. On the Homogenization of some Non-coercive Hamilton–Jacobi–Isaacs Equations. To appear in Communications on Pure and Applied Analisys.
  • A. Siconolfi, G. Terrone. A metric proof of the convers Lyapunov Theorem for semicontinuous dynamics. To appear inDiscrete and Continuous Dynamical Systems - A.
  • G. Terrone. Limiting Relaxed Controls and averaging of singularly perturbed deterministic control systems. Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical analisys, Vol. 18, n. 5 (2011), 653-672.
  • F. Cagnetti, D. Gomes, H. V. Tran: Aubry-Mather measures in the non convex setting". SIAM J. Math. Anal. 43 (2011), no. 6, 2601--2629.
  • P. Girão, M. Perez-Llanos,”Bifurcation curves for a logistic equation with harvesting orthogonal to the first eigenvalue”,submitted
  • F. Cagnetti, R. Toader: Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach. ESAIM Control Optim. Calc. Var. 17 (2011), 1--27.
  • F. Cagnetti, L. Scardia: An extension theorem in SBV and an application to the homogenization of the Mumford-Shah functional in perforated domains. J. Math. Pures Appl. 95 (2011), 349--381.
  • F. Cagnetti: k-quasi-convexity reduces to quasi-convexity. Proc. Roy. Soc. Edinburgh Sect. A 141 (2011), 673--708.
  • M. Barchiesi, F. Cagnetti, N. Fusco: Stability of the Steiner symmetrization of convex sets. To appear in J. Eur. Math. Soc.
  • F. Cagnetti, D. Gomes, H. V. Tran: Adjoint methods for obstacle problems and weakly coupled systems of PDE (submitted).
  • F. Cagnetti, D. Gomes, H. V. Tran: Convergence of a numerical scheme for the Hamilton-Jacobi equation: a new approach with the adjoint method (submitted).
  • R. de la Llave, H. Alishah, Tracking KAM tori in presymplectic dynamical systems.
  • Isabel N. Figueiredo, Surya Prasath, Yen-Hsi R. Tsai, Pedro N. Figueiredo : Colonic polyp detection in wireless capsule endoscopy images and videos, submitted (2011).
  • Juan C. Moreno, Isabel N. Figueiredo and V. B. Surya Prasath : Texture image segmentation using higher-order derivatives (10 pages), in CD-ROM Proceedings of the Congress on Numerical Methods in Engineering (CMNE|2011), Coimbra, Portugal, June 14-17, 2011.
  • Pedro N. Figueiredo, Isabel N. Figueiredo, Surya Prasath and Richard Tsai : Automatic polyp detection in PillCam COLON 2 capsule images and videos - preliminary feasibility report, Diagnostic and Therapeutic Endoscopy, in press (2011).
  • V. B. Surya Prasath, Isabel N. Figueiredo, and Pedro N. Figueiredo : Colonic mucosa detection in wireless capsule endoscopy images and videos (9 pages), in CD-ROM Proceedings of the Congress on Numerical Methods in Engineering (CMNE|2011), Coimbra, Portugal, June 14-17, 2011.
  • Isabel N. Figueiredo, Carlos Leal, Giuseppe Romanazzi, Bjorn Engquist, Pedro N. Figueiredo: A convection-diffusion-shape model for aberrant colonic crypt morphogenesis, Computing and Visualization in Science, 14, 4 (2011) 157-166.
  • Isabel N. Figueiredo, Surya Prasath, Yen-Hsi R. Tsai, Pedro N. Figueiredo: Automatic detection and segmentation of colonic polyps in wireless capsule images, Preprint 10-37, Department of Mathematics, University of Coimbra (2010) (also, ICES report 10-36 and UCLA-CAM Report 10-65).
  • Isabel N. Figueiredo, Juan Moreno, Surya Prasath, Pedro Figueiredo: A segmentation model using image gradient information and applications to endoscopic images, Preprint 10-30, Department of Mathematics, University of Coimbra (2010).
  • Isabel N. Figueiredo, Pedro N. Figueiredo, Carlos Leal and José Miguel Urbano: A mathematical model for a comprehensive approach to the dynamics of human colonic aberrant crypt foci, *Preprint 08-01* of the Department of Mathematics, University of Coimbra, 2008.
  • M. Perez Llanos and Julio Rossi. The limit as p(x) \to infinity of solutions to the inhomogeneous Dirichlet problem of the p(x)-Laplacian, Nonlinear Analysis, 73, 2027-2035, 2010.
  • M. Perez Llanos and Julio Rossi. Limits as p(x) ! 1 of p(x)-harmonic functions with non- homogeneous Neumann boundary conditions,to appear in Contemporary Mathematics.
  • M. Perez Llanos, Jose Miguel Urbano and Agnese di Castro. Limits of anisotropic and degenerate elliptic problems in collaboration with , to appear in Journal Communications on Pure and Applied Analysis.
  • M. Perez Llanos and Julio Rossi. An anisotropic innity Laplacian obtained as the limit of the anisotropic (p; q)-Laplacian.
  • Birindelli, Isabeau; Patrizi, Stefania. A Neumann eigenvalue problem for fully nonlinear operators. Discrete Contin. Dyn. Syst. 28 (2010), no. 2, 845–86
  • Achdou, Yves; Patrizi, Stefania Homogenization of first-order equations with u/e-periodic Hamiltonian: rate of convergence as e?0 and numerical methods. Math. Models Methods Appl. Sci. 21 (2011), no. 6, 1317–1353
  • Patrizi, Stefania The principal eigenvalue of the 8-Laplacian with the Neumann boundary condition. ESAIM Control Optim. Calc. Var. 17 (2011), no. 2, 575–601.
  • Isabel Figueiredo, Omar Ghattas, Georg Stadler and Medical Doctors of the research project UTAustin/MAT/0009/2008. A PDE-constrained optimization problem for image segmentation of endoscopic aberrant crypt foci.
  • Isabel Figueiredo, Georg Stadler and Medical Doctors of the research project UTAustin/MAT/0009/2008. A multiscale segmentation model for aberrant crypt foci.
  • Isabel N. Figueiredo, Juan Carlos Moreno, V. B. Surya Prasath, Pedro N. Figueiredo : A Segmentation Model and Application to Endoscopic Images, International Conference on Image Analysis and Recognition (ICIAR 2012), Aveiro, Portugal, June 25-27, 2012. Proc. in Springer LNCS 7325/2012 (eds.: A. Campilho and M. Kamel), Part II, pp. 164-171, June 2012.
  • Isabel N. Figueiredo, Juan C. Moreno, V. B. Surya Prasath. Texture Image Segmentation with Smooth Gradients and Local Information, Computational Modeling of Objects Presented in Images: Fundamentals, Methods and Applications (CompIMAGE 2012), Rome, Italy, September 5-7, 2012.
  • V. B. Surya Prasath, Isabel N. Figueiredo, Pedro N. Figueiredo, K. Palaniappan : Mucosal Region Detection and 3D Reconstruction in Wireless Capsule Endoscopy Videos Using Active Contours, 34th Annual International Conference EMBS (IEEE EMBS/EMBC 2012), San Diego, USA, August 28 - September 01, 2012.
  • Isabel Figueiredo, Bjorn Engquist, Richard Tsai, Carlos Leal, Giuseppe Romanazzi and Medical Doctors of the research project UTAustin/MAT/0009/2008. A micro-macro model for tracking the shape of colonic crypts.
  • Sílvia Barbeiro and Mary F. Wheeler: "Coupling methods for poro-elasticity", work in progress.
  • Dawson, C. and J.H. Videman, A streamline diffusion finite element method for the viscous shallow water equations. Submitted.

Other project publications (partial list)

  • C. Caputo, “Time Scales: from Nabla Calculus to Delta Calculus and vice versa via Duality”, to appear on IJDE
    • Gonçalves, P., Pereira, B. and J.H. Videman, Error estimates for a coupled continuous– discontinuous FEM for the two-layer shallow water equations. Submitted.
  • Nazarov, S.A., Taskinen, J. and J.H. Videman, Asymptotic behavior of trapped modes in a liquid with small density variations. Submitted.
  • Cal, F.S., Dias, G.A.S. and J.H. Videman, Existence of trapped modes in a periodic array of obstacles in a two-layer fluid, Q. Jl Mech. Appl. Math. 65, 273–292 (2012).
  • Chiadò Piat, V., Nazarov, S.A. and J.H. Videman, Asymptotics of frequency of a surface wave trapped by a slightly inclined barrier in a liquid layer, Zapiski Nauch. Sem. POMI, 393, 46–79 (2011).
  • Nazarov, S.A. and J.H. Videman, Trapping of water waves by freely floating structures in a channel, Proc. Roy. Soc. London A, 467, 3613–3632 (2011).
  • Nazarov, S.A. and J.H. Videman, Existence of edge waves along three-dimensional peri- odic structures, J. Fluid Mech. 659, 225–246 (2010).
    • Urbano, José Miguel; Vorotnikov, Dmitry On the well-posedness of a two-phase minimization problem. J. Math. Anal. Appl. 378 (2011), no. 1, 159–168
  • Urbano, José Miguel, T. Kuusi, R. Laleoglu and J. Siljander Hölder continuity for Trudinger's equation in measure spaces, Calc. Var. Partial Differential Equations, to appear.
  • Urbano, José Miguel, A. Di Castro and M. Pérez-Llanos Limits of anisotropic and degenerate elliptic problems Commun. Pure Appl. Anal., to appear.
  • Urbano, José Miguel, T. Kuusi and J. Siljander Local Hölder continuity for doubly nonlinear parabolic equations, Indiana Univ. Math. J., to appear.
  • Manfredi, J. J.; Rossi, J. D.; Urbano, J. M. Limits as p(x)?8 of p(x)-harmonic functions. Nonlinear Anal. 72 (2010), no. 1, 309–315
  • Gomes, D. A.; Lopes, A. O.; Mohr, J. The Mather measure and a large deviation principle for the entropy penalized method. Commun. Contemp. Math. 13 (2011), no. 2, 235–268.
  • Biryuk, Andrey; Gomes, Diogo A. An introduction to the Aubry-Mather theory. São Paulo J. Math. Sci. 4 (2010), no. 1, 17–63
  • Gomes, Diogo A.; Jung, Nara; Lopes, Artur O. Minimax probabilities for Aubry-Mather problems. Commun. Contemp. Math. 12 (2010), no. 5, 789–813.
  • Gomes, Diogo; Iturriaga, Renato; Sánchez-Morgado, Héctor; Yu, Yifeng Mather measures selected by an approximation scheme. Proc. Amer. Math. Soc. 138 (2010), no. 10
  • Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigão Discrete time, finite state space mean field games. J. Math. Pures Appl. (9) 93 (2010), no. 3, 308–328.
  • Figueiredo, Isabel N.; Figueiredo, Pedro N.; Almeida, Nuno Image-driven parameter estimation in absorption-diffusion models of chromoscopy. SIAM J. Imaging Sci. 4 (2011), no. 3, 884–904.
  • Ferreira, J. A.; de Oliveira, P.; da Silva, P. M. Mathematical analysis of waiting times for reaching therapeutic effects. CMES Comput. Model. Eng. Sci. 76 (2011), no. 3-4, 163–174.
  • Ferreira, José A.; de Oliveira, Paula; da Silva, Pascoal; Simon, Laurent Flux tracking in drug delivery. Appl. Math. Model. 35 (2011), no. 10, 4684–4696.
  • Ferreira, J. A.; de Oliveira, P.; Silva, P.; Murta, J. N. Drug delivery: from a contact lens to the anterior chamber. CMES Comput. Model. Eng. Sci. 71 (2011), no. 1, 1–14.
  • Barbeiro, S.; Ferreira, J. A.; Pinto, L. H1-second order convergent estimates for non-Fickian models. Appl. Numer. Math. 61 (2011), no. 2, 201–215.
  • Ferreira, J. A.; Mouro, A. P.; Oliveira, P. Lifting solutions of quasilinear convection-dominated problems. Int. J. Comput. Math. 87 (2010), no. 7, 1522–1537.
  • Ferreira, José Augusto; de Oliveira, Paula Looking for the lost memory in diffusion-reaction equations. Advances in mathematical fluid mechanics, 229–251, Springer, Berlin, 2010
  • Branco, J. R.; Ferreira, J. A.; da Silva, P. Non-Fickian delay reaction-diffusion equations: theoretical and numerical study. Appl. Numer. Math. 60 (2010), no. 5, 531–549
    • Bodnár, T.; Rajagopal, K. R.; Sequeira, A. Simulation of the three-dimensional flow of blood using a shear-thinning viscoelastic fluid model. Math. Model. Nat. Phenom. 6 (2011), no. 5, 1–24
  • Sequeira, Adélia; Santos, Rafael F.; Bodnár, Tomáš Blood coagulation dynamics: mathematical modeling and stability results. Math. Biosci. Eng. 8 (2011), no. 2, 425–443
  • Gambaruto, Alberto M.; Janela, João; Moura, Alexandra; Sequeira, Adélia Sensitivity of hemodynamics in a patient specific cerebral aneurysm to vascular geometry and blood rheology. Math. Biosci. Eng. 8 (2011), no. 2, 409–423
  • Bodnár, T.; Sequeira, A.; Prosi, M. On the shear-thinning and viscoelastic effects of blood flow under various flow rates. Appl. Math. Comput. 217 (2011), no. 11, 5055–5067
  • Smith, Keith D.; Sequeira, Adélia Micro-macro simulations of a shear-thinning viscoelastic kinetic model: applications to blood flow. Appl. Anal. 90 (2011), no. 1, 227–252.
  • Sellountos, Euripides J.; Sequeira, Adélia; Polyzos, Demosthenes A new LBIE method for solving elastodynamic problems. Eng. Anal. Bound. Elem. 35 (2011), no. 2, 185–190
  • Janela, João; Moura, Alexandra; Sequeira, Adélia Absorbing boundary conditions for a 3D non-Newtonian fluid-structure interaction model for blood flow in arteries. Internat. J. Engrg. Sci. 48 (2010), no. 11, 1332–1349
  • Janela, João; Moura, Alexandra; Sequeira, Adélia A 3D non-Newtonian fluid-structure interaction model for blood flow in arteries. J. Comput. Appl. Math. 234 (2010), no. 9
  • Isabel N. Figueiredo, Carlos Leal, Tommaso Leonori, Giuseppe Romanazzi, Pedro N. Figueiredo and M. Manuel Donato: A coupled convection-diffusion level set model for tracking epithelial cells in colonic crypts, Procedia Computer Science, 1, 1 (2010) 955-963