Mathematical Analysis, Modelling, and Applications | Mathematics Area - SISSA

Mathematical Analysis, Modelling, and Applications

The activity in mathematical analysis is mainly focussed on ordinary and partial differential equations, on dynamical systems, on the calculus of variations, and on control theory. Connections of these topics with differential geometry are also developed.The activity in mathematical modelling is oriented to subjects for which the main technical tools come from mathematical analysis. The present themes are multiscale analysis, mechanics of materials, micromagnetics, modelling of biological systems, and problems related to control theory.The applications of mathematics developed in this course are related to the numerical analysis of partial differential equations and of control problems. This activity is organized in collaboration with MathLab for the study of problems coming from the real world, from industrial applications, and from complex systems.

On robust Lie-algebraic stability conditions for switched linear systems

Agrachev AA, Baryshnikov Y, Liberzon D. On robust Lie-algebraic stability conditions for switched linear systems. Systems and Control Letters. Volume 61, Issue 2, February 2012, Pages 347-353 [Internet]. 2012 . Available from: http://hdl.handle.net/1963/6455

Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants

Rozza G, Huynh P, Manzoni A. Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants. Numerische Mathematik, 2013 [Internet]. 2013 . Available from: http://hdl.handle.net/1963/6339

Admissible Riemann solvers for genuinely nonlinear P-systems of mixed type

Mercier J-M, Piccoli B. Admissible Riemann solvers for genuinely nonlinear P-systems of mixed type. J. Differ. Equations, 2002, 180, 395 [Internet]. 2002 . Available from: http://hdl.handle.net/1963/1491

Diffusion time and splitting of separatrices for nearly integrable

Berti M, Bolle P. Diffusion time and splitting of separatrices for nearly integrable. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl., 2000, 11, 235 [Internet]. 2000 . Available from: http://hdl.handle.net/1963/1547

Reverse engineering the euglenoid movement

Arroyo M, Heltai L, Millán D, DeSimone A. Reverse engineering the euglenoid movement. Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879 [Internet]. 2012 . Available from: http://hdl.handle.net/1963/6444

Solving Honig generic problem about Volterra integral equations

Vidossich G. Solving Honig generic problem about Volterra integral equations. Bull. Polish Acad. Sci. Math. 44 (1996), no. 4, 495--498 [Internet]. 1996 . Available from: http://hdl.handle.net/1963/941

Morse properties for the minimum time function on 2-D manifolds

Boscain U, Piccoli B. Morse properties for the minimum time function on 2-D manifolds. J. Dynam. Control Systems 7 (2001), no. 3, 385--423 [Internet]. 2001 . Available from: http://hdl.handle.net/1963/1541

Global calibrations for the non-homogeneous Mumford-Shah functional

Morini M. Global calibrations for the non-homogeneous Mumford-Shah functional. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1 (2002) 603-648 [Internet]. 2002 . Available from: http://hdl.handle.net/1963/3089

Abnormal extremals for minimum time on the plane

Boscain U, Piccoli B. Abnormal extremals for minimum time on the plane. [Internet]. 2000 . Available from: http://hdl.handle.net/1963/1508

Local calibrations for minimizers of the Mumford-Shah functional with a triple junction

Mora MG. Local calibrations for minimizers of the Mumford-Shah functional with a triple junction. Commun. Contemp. Math. 4 (2002) 297-326 [Internet]. 2002 . Available from: http://hdl.handle.net/1963/3050

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