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. E. S. Daus, J.P. Milišić, N. Zamponi. Global existence of a two-phase flow model with cross-diffusion. ArXiv:1901.07296, accepted for publication in DCDS-B, 2019.
  2. J.P. Milišić, D. Žubrinić. Maximally singular solutions of Laplace equations.  ArXiv:1805.0258, 2018.
  3. E. S. Daus, J.P. Milišić, N. Zamponi. Analysis of a degenerate and singular volume-filling cross-diffusion system modeling biofilm growth.  ArXiv:1805.02106, 2018.

Scientific publications

  1. J.P. Milišić. The unsaturated flow in porous media with dynamic capillary pressure, Journal of differential equations, 264 (2018), 5629-5658.
  2.  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.
  3. 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.
  4. A. Juengel, J. P. Milišić. Full compressible Navier-Stokes equations for quantum fluids: derivation and numerical solution. Kinetic Related Models 4 (3), (2011).
  5. A. Juengel, J. P. Milišić. A simplified quantum energy-transport model for semiconductors. Nonlinear Analysis Series B: Real World Applications 12 (2011), 1033-1046.
  6. 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.
  7. B. Duering, D. Matthes, J. P. Milišić. A gradient flow scheme for nonlinear fourth order equations. DCDS-B 14  (2010), 935-959.
  8. A.Juengel, J. P. Milišić. A sixth-order nonlinear parabolic equation for quantum systems. SIAM J. Math. Anal. 4 (2009), 1472-1490.
  9. A. Juengel, J. P. Milišić.  Physical and numerical viscosity for quantum hydrodynamics.  Commun. Math. Sci. 5 (2007), 447-471.
  10. A. Juengel, J.P. Milišić.  Macroscopic quantum models with and without collisions. Proceedings of the Sixth International Workshop on Mathematical Aspects of Fluid and Plasma Dynamics, Kyoto, Japan. Bulletin Inst. Math. Academia Sinica 2 (2007), 251-279.
  11.  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

Personal data

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

List of select projects

  • 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. CSF (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)