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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 analysismechanics of materialsmicromagneticsmodelling 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.

Conservation Laws and Transport Problems

Research topics

  • Hyperbolic Systems of Conservation Laws in One Space Dimension
  • Fundamental theory: existence, uniqueness and continuous dependence of weak entropy admissible solutions, characterization of semigroup trajectories
  • Problems with large BV data, blow-up of BV norm, local existence and uniqueness
  • Structure of solutions, local behavior, structural stability, generalized shift-differentiability w.r.t. parameters
  • Initial-boundary problems, inhomogeneous balance laws, asymptotic blow-up patterns, global existence
  • Convergence rates for approximation schemes: wave-front tracking, Glimm, finite element
  • Vanishing viscosity approximations, a-priori estimates, convergence
  • Flow of weakly differentiable vector fields
  • Linear transport problems

Dynamical Systems and PDEs

Research topics

  • KAM for PDEs
  • Water waves, KdV, Schrödinger and Klein-Gordon equations
  • Hamiltonian systems
  • Birkhoff normal form for PDEs and long time existence
  • Chaotic Dynamics and Arnold Diffusion
  • Variational Methods
  • Perturbative Methods in Critical Point Theory

 

Research Group

Visiting Professors

 

Main External Collaborators

 

Grants

Mathematical Analysis, Modelling, and Applications

A research group in mathematical analysis has been active at SISSA since 1978, the year SISSA was founded. Starting from 2000, the activity of this group has been extended to mathematical modelling and applications. 

 

Research Topics

The activity in mathematical analysis is mainly focused on Dynamical Systems and PDEs, on the Calculus of Variations, on Hyperbolic Conservation Laws and Transport Problems, on Geometric Analysis and on Geometry and Control theory. Connections of these topics with differential geometry and reduced order modeling 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 analysismechanics of materialscell motility and mechano-biologymicromagneticsmodelling of biological systems, computational fluid and solid dynamics 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.

Faculty

Former Faculty Members

Former Professors

Visiting Professors

External Collaborators

Temporary Scientific Staff

Seminars

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Events and Workshops

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Publications

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