izv. prof. dr. sc. Josipa Pina Milišić

Associate professor, Department of Applied Mathematics


 Summer term 2019, Friday 12:00 - 13:00

Public phone number:
+385 1 6129 939
Internal phone number:


  1. J.P. Milišić, D. Žubrinić. Maximally singular solutions of Laplace equations.  ArXiv:1805.0258, accepted for publication in RMJ, https://rmmc.eas.asu.edu/rmj/rmj.html

Scientific publications

  1. E. S. Daus, J.P. Milišić, N. Zamponi. Global existence of a two-phase flow model with cross-diffusion, DCDS-B,  25 (3) (2020), 957-979.
  2. E. S. Daus, J.P. Milišić, N. Zamponi. Analysis of a degenerate and singular volume-filling cross-diffusion system modeling biofilm growth,  SIAM J. Math. Anal., 51 (4) (2019), 3569–3605.
  3. J.P. Milišić. The unsaturated flow in porous media with dynamic capillary pressure, Journal of differential equations, 264 (2018), 5629-5658.
  4.  A. Juengel, J. P. Milišić. Entropy dissipative one-leg multistep time approximations of nonlinear diffusive equations, Numer. Meth. Part. Diff. Eqs. 31 (2015), 1119-1149.
  5. B. Amaziane, J. P. Milišić, M. Panfilov, L. Pankratov. Generalized nonequilibrium capillary relations for two-phase flow through heterogeneous media, Physical Review E 85 (2012), 18 pages.
  6. A. Juengel, J. P. Milišić. Full compressible Navier-Stokes equations for quantum fluids: derivation and numerical solution. Kinetic Related Models 4 (3), (2011).
  7. A. Juengel, J. P. Milišić. A simplified quantum energy-transport model for semiconductors. Nonlinear Analysis Series B: Real World Applications 12 (2011), 1033-1046.
  8. J.P. Milišić, D. Žubrinić, V. Županović. Fractal analysis of Hopf bifurcation for a class of completely integrable nonlinear Schroedinger equation. EQJDE 60 (2010), 1-32.
  9. B. Duering, D. Matthes, J. P. Milišić. A gradient flow scheme for nonlinear fourth order equations. DCDS-B 14  (2010), 935-959.
  10. A.Juengel, J. P. Milišić. A sixth-order nonlinear parabolic equation for quantum systems. SIAM J. Math. Anal. 4 (2009), 1472-1490.
  11. A. Juengel, J. P. Milišić.  Physical and numerical viscosity for quantum hydrodynamics.  Commun. Math. Sci. 5 (2007), 447-471.
  12. A. Juengel, J.P. Milišić.  Macroscopic quantum models with and without collisions. Bulletin Inst. Math. Academia Sinica 2 (2007), 251-279.
  13.  A. Juengel, D. Matthes, J.P. Milišić.  Derivation of new quantum hydrodynamic equations using entropy minimization. SIAM J. Appl. Math. 67 (2006), 46-68.

Conference proceedings

  1. A. Juengel, J. P. Milišić. Quantum Navier-Stokes equations. Progress in Industrial Mathematics at ECMI 2010, Mathematics in Industry, Vol. 17, Guenther, M.; Bartel, A.; Brunk, M.; Schoeps, S.; Striebel, M. (Eds.), Januar 2012.


Research interests

  • Entropy methods for nonlinear diffusive PDEs with cross-diffusion structure
  • Analysis of multi-component fluid models
  • Multiphase flows in porous media


  • 2003 -- 2007  Ph.D. in Applied Mathematics, University of Mainz, Germany. Ph.D. thesis: Quantum Hydrodynamic Models for Semiconductors with and without Collisions (Advisor: A. Juengel)
  • 1999 -- 2003 Postgraduate study in Applied Mathematics, University of Zagreb, Croatia. M.Sc. thesis: Continuity of Weak Solutions of Quasilinear Elliptic Equations (Advisor: M. Pašić)
  • 1992 -- 1998 Graduate study in Applied Mathematics, University of Zagreb, Croatia. Diploma thesis: Stability of Stationary Solutions for an Ideal Fluid (Advisor: I. Aganović)


  • May 2019 --  today       Associate Professor, UniZg-FER
  • May 2014 -- Apr 2019  Associate Professor, UniZg-FER
  • May 2009 -- Apr 2014  Assistant Professor, UniZg-FER
  • Sep  2007 -- Apr 2009  Research and Teaching Assistant, UniZg-FER
  • Sep  2003 -- Aug 2007 Research Associate, Department of Physics,  Mathematics and Computer Science, JoGu-Mainz, Germany
  • Mar  2002 -- Aug 2003 Research and Teaching Assistant, UniZg-FER
  • Sep  2001 -- Feb 2002  UniZg-SRCE
  • Jul   1999 -- Aug 2001  Teaching Assistant, Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Croatia

Teaching duties

University undergraduate

University graduate

Postgraduate doctoral study programme


  • Mathematics
    Partial differential equations Nonlinear systems Numerical analysis
  • Electron devices
    Semiconductor device modeling Resonant tunneling devices

Personal data

Graduation year:
mr.sc. graduation year:
PhD graduation year:
Employed in this institution since:

List of select projects

  • 2020 -- 2024 Research Associate. Multiscale problems in fluid mechanics. HRZZ (PI: I. Pažanin)
  • 2018 -- 2020 Research Associate. Multi-species biofilm diffusion systems for wastewater treatment. MZOS and OEAD (bilateral project, PI: M.Bukal)
  • 2016 -- 2018 Project Leader. Mathematical and Numerical Analysis of Cross-Diffusion Models in Biology. MZOS and OEAD
  • 2014 -- 2018 Research Associate. Mathematical Modelling and Numerical Simulations of Processes in Thin or Porous Domains. HRZZ (PI: E. Marušić-Paloka)
  • 2010 -- 2011 Research Associate. Modelisation mathematique et simulation numerique de la migration de Gaz dans le systeeme d'un stockage souterrain de dechets radioactifs. MoMaS, France 
  • 2010 -- 2011 Project Leader. Kinetic wealth distribution models and diffusive limit equations. MZOS and OEAD (bilateral project)
  • 2008 -- 2009 Project Leader. Viscous approximations of quantum Euler-Poisson systems. MZOS and OEAD (bilateral project)
  • 2007 -- 2009 Research Associate. Nonlinear analysis of differential equations and dynamical systems. MZOS (PI: M. Pašić)
  • 2003 -- 2007 Research Associate. Mathematical analysis and  numerical approximations of macroscopic models for semiconductors and plasmas. German Exchange Service DAAD (PI: A. Juengel)
  • 2001 -- 2003 Research Associate. Nonlinear analysis of differential equations. MZOS (PI: M. Pašić)