Andrea Signori, PhD, AvH Fellow

Department of MathematicsPolitecnico di Milano • Via E. Bonardi 9, 20133 Milano, Italy • andrea.signori@polimi.it


Publications (Last Update: 20/07/22, reverse chronological order)

Recent Preprints

  1. P. Colli, G. Gilardi, A. Signori and J. Sprekels, On a Cahn–Hilliard system with source term and thermal memory.
    Preprint arXiv:2207.08491 [math.AP], (2022), 1-28.    WIAS Preprint.
  2. H. Garcke, K. F. Lam, R. Nürnberg and A. Signori, Phase field topology optimisation for 4D printing.
    Preprint arXiv:2207.03706 [math.OC], (2022), 1-41.
  3. P. Colli, G. Gilardi, A. Signori and J. Sprekels, Optimal control of a nonconserved phase field model of Caginalp type with thermal memory and double obstacle potential.
    Preprint arXiv:2207.00375 [math.OC], (2022), 1-23.    WIAS Preprint.
  4. P. Colli, G. Gilardi, A. Signori and J. Sprekels, Cahn–Hilliard–Brinkman model for tumor growth with possibly singular potentials.
    Preprint arXiv:2204.13526 [math.AP], (2022), 1-31.    WIAS Preprint.
  5. M. Grasselli, L. Scarpa and A. Signori, On a phase field model for RNA-Protein dynamics.
    Preprint arXiv:2203.03258 [math.AP], (2022), 1-54.
  6. E. Rocca, G. Schimperna and A. Signori, On a Cahn–Hilliard–Keller–Segel model with generalized logistic source describing tumor growth.
    Preprint arXiv:2202.11007 [math.AP], (2022), 1-38.
  7. H. Garcke, K. F. Lam, R. Nürnberg and A. Signori, Overhang penalization in additive manufacturing via phase field structural topology optimization with anisotropic energies.
    Preprint arXiv:2111.14070 [math.OC], (2021), 1-41.

Published Papers

  1. P. Colli, A. Signori and J. Sprekels, Analysis and optimal control theory for a phase field model of Caginalp type with thermal memory.
    Commun. Optim. Theory, 4 (2022).
    doi.org/10.23952/cot.2022.4.    Preprint arXiv:2107.09565 [math.OC].    WIAS Preprint.
  2. P. Colli, A. Signori and J. Sprekels, Optimal control problems with sparsity for phase field tumor growth models involving variational inequalities. J. Optim. Theory Appl., (2022).
    doi.org/10.1007/s10957-022-02000-7.    Preprint arXiv:2104.09814 [math.OC].    WIAS Preprint.
  3. E. Rocca, L. Scarpa and A. Signori, Parameter identification for nonlocal phase field models for tumor growth via optimal control and asymptotic analysis. Math. Models Methods Appl. Sci., 31(13) (2021), 2643-2694.
    doi.org/10.1142/S0218202521500585.    Preprint arXiv:2009.11159 [math.AP].
  4. P. Knopf and A. Signori, Existence of weak solutions to multiphase Cahn–Hilliard–Darcy and Cahn–Hilliard–Brinkman models for stratified tumor growth with chemotaxis and general source terms. Comm. Partial Differential Equations, 47(2) (2022), 233-278.
    doi.org/10.1080/03605302.2021.1966803.    Preprint arXiv:2105.09068 [math.AP].
  5. P. Colli, A. Signori and J. Sprekels, Second-order analysis of an optimal control problem in a phase field tumor growth model with singular potentials and chemotaxis. ESAIM Control Optim. Calc. Var., 27 (2021).
    doi.org/10.1051/cocv/2021072.    Preprint arXiv:2009.07574 [math.AP].    WIAS Preprint.
  6. L. Scarpa and A. Signori, On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport. Nonlinearity, 34 (2021), 3199-3250.
    doi.org/10.1088/1361-6544/abe75d.    Preprint arXiv:2002.12702 [math.AP].
  7. H. Garcke, K. F. Lam and A. Signori, Sparse optimal control of a phase field tumour model with mechanical effects.
    SIAM J. Control Optim., 59(2) (2021), 1555-1580.
    doi.org/10.1137/20M1372093.    Preprint arXiv:2010.03767 [math.OC].
  8. S. Frigeri, K. F. Lam and A. Signori, Strong well-posedness and inverse identification problem of a non-local phase field tumor model with degenerate mobilities. European J. Appl. Math., 33(2) (2022), 267-308.
    doi:10.1017/S0956792521000012.    Preprint arXiv:2004.04537 [math.AP].
  9. P. Knopf and A. Signori, On the nonlocal Cahn–Hilliard equation with nonlocal dynamic boundary condition and boundary penalization.
    J. Differential Equations, 280(4) (2021), 236-291.
    doi.org/10.1016/j.jde.2021.01.012.    Preprint arXiv:2004.00093 [math.AP].
  10. H. Garcke, K. F. Lam and A. Signori, On a phase field model of Cahn–Hilliard type for tumour growth with mechanical effects.
    Nonlinear Anal. Real World Appl., 57 (2021), 103192.
    doi.org/10.1016/j.nonrwa.2020.103192.    Preprint arXiv:1912.01945 [math.AP].
  11. P. Colli, A. Signori and J. Sprekels, Optimal control of a phase field system modelling tumor growth with chemotaxis and singular potentials.
    Appl. Math. Optim., 83 (2021), 2017-2049.
    doi.org/10.1007/s00245-019-09618-6   (see also the Erratum).    Preprint arXiv:1907.03566 [math.AP].    WIAS Preprint.
  12. P. Colli and A. Signori, Boundary control problem and optimality conditions for the Cahn–Hilliard equation with dynamic boundary conditions.
    Internat. J. Control, 94 (2021), 1852-1869.
    doi.org/10.1080/00207179.2019.1680870.    Preprint arXiv:1905.00203 [math.AP].
  13. A. Signori, Penalisation of long treatment time and optimal control of a tumour growth model of Cahn–Hilliard type with singular potential.
    Discrete Contin. Dyn. Syst. Ser. A, 41(6) (2021), 2519-2542.
    doi.org/10.3934/dcds.2020373.    Preprint arXiv:1906.03460 [math.AP].
  14. A. Signori, Vanishing parameter for an optimal control problem modeling tumor growth.
    Asymptot. Anal., 117 (2020), 43-66.
    doi.org/10.3233/ASY-191546.    Preprint arXiv:1903.04930 [math.AP].
  15. A. Signori, Optimal treatment for a phase field system of Cahn–Hilliard type modeling tumor growth by asymptotic scheme.
    Math. Control Relat. Fields, 10 (2020), 305-331.
    doi:10.3934/mcrf.2019040.    Preprint arXiv:1902.01079 [math.AP].
  16. A. Signori, Optimality conditions for an extended tumor growth model with double obstacle potential via deep quench approach.
    Evol. Equ. Control Theory, 9(1) (2020), 193-217.
    doi:10.3934/eect.2020003.    Preprint arXiv:1811.08626 [math.AP].
  17. A. Signori, Optimal distributed control of an extended model of tumor growth with logarithmic potential.
    Appl. Math. Optim., 82 (2020), 517-549.
    doi.org/10.1007/s00245-018-9538-1.    Preprint arXiv:1809.06834 [math.AP].

  18. PhD Thesis: A. Signori, Understanding the Evolution of Tumours, a Phase-field Approach: Analytic Results and Optimal Control, 2020.
    (Doctoral advisor: Prof. Pierluigi Colli, Università di Pavia).

Research interests

phase-field based Tumor growth models

Cancer is still nowadays one of the leading causes of death worldwide. The understanding of the development of solid tumour growth is doubtless one of the main challenges of the current century. In this framework, mathematics could play a crucial role as multiscale mathematical modelling provides a quantitative tool that may help in diagnostic and prognostic applications. For these reasons, nonlinear PDEs open the doors for a concrete interaction between the experimental method used by the doctors and the more theoretical one of mathematics as numerical solvers may be implemented as a supporting tool in clinical therapies. The core of the phase-field based models I am interested in consists of a coupling of a Cahn–Hilliard type equation with source term, which takes into account cell-to-cell adhesion effects, with a reaction-diffusion equation for some surrounding species acting as a nutrient.

Biological models

Phase separation has recently become a paradigm in Cell Biology and, in particular, in the intracellular organization. In this direction, I would like to mention protein-RNA complexes models. The ingredients are a protein, two RNA species, and two protein-RNA complexes. The interaction of the protein with the RNA species in a given solvent is ruled by a coupled system of reaction-diffusion equations, while the reaction terms depend on all the variables. The complexes instead are governed by a system of Cahn–Hilliard equations with reaction terms. Another biological mechanism I got interested in recently is chemotaxis along with the celebrated Keller–Segel model.

Optimal control for PDE

Optimal control theory aims at finding the smarter choice to address the solution of a problem (system of PDEs) by minimising suitable quantities which may represent, in a general sense, some costs. For this latter, a prototypical choice is a tracking-type cost functional which allows to "force" the system to approximate suitable targets. Typical questions arising in optimal control theory concerns the existence of optimal strategies and optimality conditions for minimisers.

Topological optimisation and Linear elasticity

A combination between phase-field approach and optimal control theory proves very effective in solving structural topological optimisation problems. In this direction, we point out that the basic equations behind those problems are coming from linear elasticity theory. A meaningful application concern additive manufacturing. This is building technique that produces objects in a layer-by-layer fashion through fusing or binding raw materials in powder and resin forms. Since its introduction in the 1970s, it has shown great versatility in allowing for the creation of highly complex geometries, immediate modifications, and redesign, thus making it an ideal process for rapid prototyping and testing. However, despite its great employment in real-world applications, lots of theoretical issues are still left to be clarified.

Dynamic boundary conditions

In some physical scenarios, it turned out that the standard Neumann and Dirichlet boundary conditions (as well as of the third type) are not completely satisfactory as they neglect the influence of certain processes on the boundary to the dynamics in the bulk. Hence, the need to include some nontrivial dynamics in the boundary through some dynamic boundary conditions.

Education



Non-tenure track Assistant Professor RTDa (Politecnico di Milano)

July 2022 - Today

Postdoctoral Researcher (University of Pavia)

March 2021 - July 2022

Doctorate in Mathematics (University of Milano-Bicocca)

Title of the Thesis: Understanding the Evolution of Tumours, a Phase-field Approach: Analytic Results and Optimal Control (supervisor: Prof. Pierluigi Colli).

During my third year of PhD (15/09/19-15/12/19) I had the privilege to be a guest for three months of
Prof. Dr. Harald Garcke at the University of Regensburg.
October 2017 - December 2020

Master of Science in Mathematics (University of Pavia)

Title of the thesis: Boundary control problem and optimality conditions for the Cahn-Hilliard equation with dynamic boundary conditions (supervisor: Prof. Pierluigi Colli), 110/110 cum Laude.

September 2015 - September 2017

Bachelor of Science in Mathematics (University of Pavia)

Title of the thesis: The Legendre-Fenchel transform (supervisor: Prof. Enrico Vitali).

September 2012 - September 2015

Teaching


Politecnico of Milan


Adjunct Professor: Mathematics with elements of Statistic, degree course in Pharmacy (University of Pavia)

A.Y. 2022 - 2023

Exercise lectures: Mathematical and Numerical Methods in Engineering, Master Degree Program in Biomedical Engineering

A.Y. 2022 - 2023

University of Pavia


Adjunct Professor: Mathematics with elements of Statistic, degree course in Pharmacy

A.Y. 2021 - 2022

Exercise lectures: Calculus 2, 4 hours, degree course in Engineering

A.Y. 2020 - 2021

Exercise lectures: Elements of Mathematics and statistic, 12 hours, degree course in Science, technology and environment

A.Y. 2020 - 2021

Seminar lectures: Precorsi, 20 hours, degree course in Engineering

A.Y. 2019 - 2020

Exercise lectures: Advanced Calculus and Statistic, 7 hours, degree course in Engineering

A.Y. 2018 - 2019

Project: Lauree PLS, Il gioco e il Caso, 30 hours

A.Y. 2018 - 2019

Exercise lectures: Calculus 2, 10 hours, degree course in Physics

A.Y. 2018 - 2019

Exercise lectures: Calculus 1, 10 hours, degree course in Engineering

A.Y. 2018 - 2019

Exercise lectures: Elements of Mathematics and statistic, 14 hours, degree course in Science, technology and environment

A.Y. 2018 - 2019

Exercise lectures: Mathematics and statistic, 6 hours, degree course in Biotechnology

A.Y. 2018 - 2019

Exercise lectures: Mathematics, 20 hours, degree course in Biotechnology

A.Y. 2017 - 2018

Exercise lectures: Mathematics, 15 hours, degree course in Biotechnology

A.Y. 2017 - 2018

Exercise lectures: Calculus 2, 28 hours, degree course in Engineering

A.Y. 2016 - 2017

Exercise lectures: Mathematics, 20 hours, degree course in Biotechnology

A.Y. 2015 - 2016

Invited Talks and seminars




Collaborators


My Erdős number is 4 with paths being: Paul Erdős - Vilmos Komornik - Dan Tiba - Jürgen Sprekels - Signori Andrea,
or
Paul Erdős - Vilmos Komornik - Masahiro Yamamoto - Maurizio Grasselli - Signori Andrea.