Robust and scalable nonlinear solvers for finite element discretizations of biological transportation networks.

Peter A. Markowich

Jan Haskovec Peter A. Markowich Simone Portaro Stefano Zampini Robust and scalable nonlinear solvers for finite element discretizations of biological transportation networks. 2025 April abs/2504.04447 CoRR https://doi.org/10.48550/arXiv.2504.04447 db/journals/corr/corr2504.html#abs-2504-04447 streams/journals/corr

Jan Haskovec Peter A. Markowich Stefano Zampini Gradient Flows for the p-Laplacian Arising from Biological Network Models: A Novel Dynamical Relaxation Approach. 2025 October abs/2510.15379 CoRR https://doi.org/10.48550/arXiv.2510.15379 db/journals/corr/corr2510.html#abs-2510-15379 streams/journals/corr

Clarissa Astuto Peter A. Markowich Simone Portaro Giovanni Russo 0001 Self-regulated biological transportation structures with general entropy dissipation: 2D case and leaf-shaped domain. 2024 abs/2408.15680 CoRR https://doi.org/10.48550/arXiv.2408.15680 db/journals/corr/corr2408.html#abs-2408-15680 streams/journals/corr

Clarissa Astuto Daniele Boffi Jan Haskovec Peter A. Markowich Giovanni Russo 0001 Asymmetry and condition number of an elliptic-parabolic system for biological network formation. 2023 abs/2301.12926 CoRR https://doi.org/10.48550/arXiv.2301.12926 db/journals/corr/corr2301.html#abs-2301-12926

Debora Amadori Boris P. Andreianov Marco Di Francesco Simone Fagioli Théo Girard Paola Goatin Peter A. Markowich Jan-Frederik Pietschmann Massimiliano D. Rosini Giovanni Russo Graziano Stivaletta Marie-Therese Wolfram The mathematical theory of Hughes' model: a survey of results. 2023 abs/2305.10076 CoRR https://doi.org/10.48550/arXiv.2305.10076 db/journals/corr/corr2305.html#abs-2305-10076

Clarissa Astuto Jan Haskovec Peter A. Markowich Simone Portaro Self-regulated biological transportation structures with general entropy dissipations, part I: the 1D case. 2023 abs/2307.16436 CoRR https://doi.org/10.48550/arXiv.2307.16436 db/journals/corr/corr2307.html#abs-2307-16436

Clarissa Astuto Daniele Boffi Jan Haskovec Peter A. Markowich Giovanni Russo 0001 Comparison of two aspects of a PDE model for biological network formation. 2022 abs/2209.08292 CoRR https://doi.org/10.48550/arXiv.2209.08292 db/journals/corr/corr2209.html#abs-2209-08292

Martin Burger 0001 Heinz W. Engl Antonio Leitão Peter A. Markowich On inverse problems for semiconductor equations. 2020 abs/2011.11370 CoRR https://arxiv.org/abs/2011.11370 db/journals/corr/corr2011.html#abs-2011-11370

A. Leitao Peter A. Markowich Jorge P. Zubelli On inverse doping profile problems for the stationary voltage-current map. 2020 abs/2011.12200 CoRR https://arxiv.org/abs/2011.12200 db/journals/corr/corr2011.html#abs-2011-12200

A. Leitao Peter A. Markowich Jorge P. Zubelli Inverse problems for semiconductors: models and methods. 2020 abs/2011.12800 CoRR https://arxiv.org/abs/2011.12800 db/journals/corr/corr2011.html#abs-2011-12800

Jan Haskovec Sabine Hittmeir Peter A. Markowich Alexander Mielke Decay to Equilibrium for Energy-Reaction-Diffusion Systems. 1037-1075 2018 50 SIAM J. Math. Anal. 1 https://doi.org/10.1137/16M1062065 db/journals/siamma/siamma50.html#HaskovecHMM18

Peter A. Markowich Josef Teichmann Marie-Therese Wolfram Parabolic Free Boundary Price Formation Models Under Market Size Fluctuations. 1211-1237 2016 14 Multiscale Model. Simul. 4 https://doi.org/10.1137/16M1066099 db/journals/mmas/mmas14.html#MarkowichTW16

Jesús Sierra Aslan R. Kasimov Peter A. Markowich Rada-Maria Weishäupl On the Gross-Pitaevskii Equation with Pumping and Decay: Stationary States and Their Stability. 709-739 2015 25 J. Nonlinear Sci. 3 https://doi.org/10.1007/s00332-015-9239-8 db/journals/jns/jns25.html#SierraKMW15

Paolo Antonelli Agissilaos Athanassoulis Zhongyi Huang Peter A. Markowich Numerical Simulations of X-Ray Free Electron Lasers (XFEL). 1607-1621 2014 12 Multiscale Model. Simul. 4 https://doi.org/10.1137/130927838 https://www.wikidata.org/entity/Q62473053 db/journals/mmas/mmas12.html#AntonelliAHM14

Michael Hintermüller Daniel Marahrens Peter A. Markowich Christof Sparber Optimal Bilinear Control of Gross-Pitaevskii Equations. 2509-2543 2013 51 SIAM J. Control. Optim. 3 https://doi.org/10.1137/120866233 https://www.wikidata.org/entity/Q115155152 db/journals/siamco/siamco51.html#HintermullerMMS13

Martin Burger 0001 Marco Di Francesco Peter A. Markowich Marie-Therese Wolfram On a mean field game optimal control approach modeling fast exit scenarios in human crowds. 3128-3133 2013 CDC https://doi.org/10.1109/CDC.2013.6760360 conf/cdc/2013 db/conf/cdc/cdc2013.html#BurgerFMW13

Shi Jin 0003 Peter A. Markowich Christof Sparber Mathematical and computational methods for semiclassical Schrödinger equations. 121-209 2011 20 Acta Numer. https://doi.org/10.1017/S0962492911000031 db/journals/actanum/actanum20.html#JinMS11

Benoit Perthame Peter A. Markowich Jorge P. Zubelli Mathematical methods and modelling of biophysical phenomena. 1359-1362 2011 53 Math. Comput. Model. 7-8 https://doi.org/10.1016/j.mcm.2010.07.012 https://www.wikidata.org/entity/Q60502800 db/journals/mcm/mcm53.html#PerthameMZ11

Benoit Perthame Peter A. Markowich Jorge P. Zubelli Mathematical methods and modeling of biophysical phenomena. 663-665 2008 47 Math. Comput. Model. 7-8 https://doi.org/10.1016/j.mcm.2007.06.001 https://www.wikidata.org/entity/Q60502844 db/journals/mcm/mcm47.html#PerthameMZ08

Zhongyi Huang Shi Jin 0003 Peter A. Markowich Christof Sparber Numerical Simulation of the Nonlinear Schrödinger Equation with Multidimensional Periodic Potentials. 539-564 2008 7 Multiscale Model. Simul. 2 https://doi.org/10.1137/070699433 db/journals/mmas/mmas7.html#HuangJMS08

Peter A. Markowich Applied partial differential equations - a visual approach. I-IX, 1-206 Springer 2007 http://www.springerlink.com/content/978-3-540-34645-6

Weizhu Bao Yunyi Ge Dieter Jaksch Peter A. Markowich Rada-Maria Weishäupl Convergence rate of dimension reduction in Bose-Einstein condensates. 832-850 2007 177 Comput. Phys. Commun. 11 https://doi.org/10.1016/j.cpc.2007.06.015 db/journals/cphysics/cphysics177.html#BaoGJMW07

Christian Klein 0002 Christof Sparber Peter A. Markowich Numerical Study of Oscillatory Regimes in the Kadomtsev-Petviashvili Equation. 429-470 2007 17 J. Nonlinear Sci. 5 https://doi.org/10.1007/s00332-007-9001-y db/journals/jns/jns17.html#KleinSM07

Zhongyi Huang Shi Jin 0003 Peter A. Markowich Christof Sparber A Bloch Decomposition-Based Split-Step Pseudospectral Method for Quantum Dynamics with Periodic Potentials. 515-538 2007 29 SIAM J. Sci. Comput. 2 https://doi.org/10.1137/060652026 db/journals/siamsc/siamsc29.html#HuangJMS07

Shu Wang Zhouping Xin Peter A. Markowich Quasi-neutral Limit of the Drift Diffusion Models for Semiconductors: The Case of General Sign-Changing Doping Profile. 1854-1889 2006 37 SIAM J. Math. Anal. 6 https://doi.org/10.1137/S0036141004440010 db/journals/siamma/siamma37.html#WangXM06

Peter A. Markowich Lorenzo Pareschi Fast conservative and entropic numerical methods for the Boson Boltzmann equation. 509-532 2005 99 Numerische Mathematik 3 https://doi.org/10.1007/s00211-004-0570-5 db/journals/nm/nm99.html#MarkowichP05

Weizhu Bao Shi Jin 0003 Peter A. Markowich Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes. 27-64 2003 25 SIAM J. Sci. Comput. 1 https://doi.org/10.1137/S1064827501393253 db/journals/siamsc/siamsc25.html#BaoJM03

Peter A. Markowich Paola Pietra Carsten Pohl Hans Peter Stimming A Wigner-Measure Analysis of the Dufort-Frankel Scheme for the Schrödinger Equation. 1281-1310 2002 40 SIAM J. Numer. Anal. 4 https://doi.org/10.1137/S0036142900381734 db/journals/siamnum/siamnum40.html#MarkowichPPS02

Peter A. Markowich Paola Pietra Carsten Pohl Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit. 595-630 1999 81 Numerische Mathematik 4 https://doi.org/10.1007/s002110050406 db/journals/nm/nm81.html#MarkowichPP99

Florian Frommlet Peter A. Markowich Christian A. Ringhofer A Wignerfunction Approach to Phonon Scattering. 339-350 1999 9 VLSI Design 4 https://doi.org/10.1155/1999/30381 db/journals/vlsi/vlsi9.html#FrommletMR99

Ingenuin Gasser Peter A. Markowich Benoit Perthame Dispersion Lemmas Revisited. 365-375 1999 9 VLSI Design 4 https://doi.org/10.1155/1999/81341 https://www.wikidata.org/entity/Q125040725 db/journals/vlsi/vlsi9.html#GasserMP99

Peter A. Markowich Paola Pietra Carsten Pohl Semiclassical Analysis of Discretizations of Schrödinger-type Equations. 397-413 1999 9 VLSI Design 4 https://doi.org/10.1155/1999/42190 db/journals/vlsi/vlsi9.html#MarkowichPP99

Debora Amadori Boris P. Andreianov Paolo Antonelli Clarissa Astuto Agissilaos Athanassoulis Weizhu Bao Daniele Boffi Martin Burger 0001 Heinz W. Engl Simone Fagioli Marco Di Francesco Florian Frommlet Ingenuin Gasser Yunyi Ge Théo Girard Paola Goatin Jan Haskovec Michael Hintermüller Sabine Hittmeir Zhongyi Huang Dieter Jaksch Shi Jin 0003 Aslan R. Kasimov Christian Klein 0002 A. Leitao Antonio Leitão Daniel Marahrens Alexander Mielke Lorenzo Pareschi Benoit Perthame Paola Pietra Jan-Frederik Pietschmann Carsten Pohl Simone Portaro Christian A. Ringhofer Massimiliano D. Rosini Giovanni Russo Giovanni Russo 0001 Jesús Sierra Christof Sparber Hans Peter Stimming Graziano Stivaletta Josef Teichmann Shu Wang Rada-Maria Weishäupl Marie-Therese Wolfram Zhouping Xin Stefano Zampini Jorge P. Zubelli