Address: 

PD Dr. habil. Mathias Wilke
Martin-Luther-Universität Halle-Wittenberg
Naturwissenschaftliche Fakultät II
Institut für Mathematik
06099 Halle (Saale)

Research interests:

• Systems of nonlinear partial differential equations, nonlinear evolution equations, dynamical systems
  

• Well-posedness, qualitative behaviour of solutions, stability properties, (optimal) regularity of solutions
  

• Free boundary problems, two-phase problems, contact angle problems

• Applications:
  

  • Mathematical fluid dynamics (e.g. incompressible Navier-Stokes)
    
  • Phase transitions (e.g. Stefan problems, Cahn-Hilliard type equations)
    
  • Reaction-Diffusion systems (e.g. of Maxwell-Stefan type)
    
  • Nonlinear Thermoelasticity
    
  • Propagation of acoustic waves (e.g. Westervelt equation, Kuznetsov equation)
    

   
  

Publications:

1. Gewöhnliche Differentialgleichungen und dynamische Systeme,
   Grundstudium Mathematik, Birkhäuser Verlag, Basel, 2010. xiv+320 pp. ISBN: 978-3-0348-0001-3 (with J. Prüss).
   
   
2. Gewöhnliche Differentialgleichungen und dynamische Systeme, 2nd, revised and extended edition,
   Grundstudium Mathematik, Birkhäuser Verlag, Basel, 2019. xvii+432 pp. ISBN: 978-3-030-12361-1 (with J. Prüss).

Articles (all peer-reviewed):

1. Maximal Lp - Regularity and Long - Time Behaviour of the Non-Isothermal Cahn-Hilliard Equation with Dynamic Boundary Conditions,
   Operator Theory: Advances and Applications 168,  209-236, Birkhäuser, Basel, 2006 (with J. Prüss).
   

2. Convergence to Equilibrium for the Cahn-Hilliard Equation with a Logarithmic Free Energy,
   Nonlinear Analysis TMA 67, 3176-3193, 2007, (pdf-file of preprint-version), (with H. Abels).
   

3. An Analysis of Asian Options,
   Functional Analysis and Evolution Equations, 547-559, Birkhäuser,  Basel, 2007 (with S. Sperlich, J. Prüss). 
   

4. Fractional white noise perturbations of parabolic Volterra equations,
   Journal of Applied Analysis 16, 31-48, 2010 (with S. Sperlich).
   

5. On quasilinear parabolic evolution equations in weighted Lp spaces,
   Journal of Evolution Equations 10, 443-463, 2010 (Link to preprint version), (with M. Köhne, J. Prüss).
   

6. On Conserved Penrose-Fife type Models,
   Progress in Nonlinear Differential Equations and Their Applications 80, 541-576, 2011, (Link to preprint version), (with J. Prüss). 
   

7. Optimal regularity and long-time behavior of solutions for the Westervelt equation,
   Applied Mathematics and Optimization 64, 257-271, 2011, (Link to preprint version), (with St. Meyer).
   

8. Lp-theory for a Cahn-Hilliard-Gurtin system,
   Evolution Equations and Control Theory 1, 393-429, 2012, (Link to preprint version).
   

9. Invariant foliations near normally hyperbolic equilibria for quasilinear parabolic problems,
   Advanced Nonlinear Studies 13, 231-244, 2013, (Link to preprint version), (with J. Prüß, G. Simonett).
   

10. Global well-posedness and exponential stability for Kuznetsov's equation in Lp-spaces,
    Evolution Equations and Control Theory 2, 365-378, 2013, (Link to preprint version), (with St. Meyer).
    

11. Qualitative Behaviour of Solutions for the Two-Phase Navier-Stokes Equations with Surface Tension,
    Mathematische Annalen 356, 737-792, 2013, (Link to preprint version), (with M. Köhne, J. Prüss).
    

12. Maximal regularity and global existence of solutions to a quasilinear thermoelastic plate system,
    Discrete and Continuous Dynamical Systems A, 33, 5189 - 5202, 2013, (Link to preprint version), (with I. Lasiecka).
    

13. Well-Posedness and Qualitative Behaviour of Solutions for the Two-Phase Navier-Stokes-Mullins-Sekerka Equations,
    Interfaces and Free Boundaries 15, 39-75, 2013, (Link to preprint version), (with H. Abels).
     

14. Qualitative behaviour of incompressible two-phase flows with phase transitions: The case of non-equal densities,
    Communications in Partial Differential Equations 39, 1236–1283, 2014, (Link to preprint version), (with J. Prüss, S Shimizu).
    

15. On quasilinear parabolic evolution equations in weighted Lp-spaces II,
    Journal of Evolution Equations 14, 509–533, 2014, (Link to preprint version), (with J. LeCrone, J. Prüss).
    

16. On thermodynamically consistent Stefan problems with variable surface energy,
    Archive for Rational Mechanics and Analysis 202, 603-638, 2016 (Link to preprint version), (with J. Prüss, G. Simonett).

17. On incompressible two-phase flows with phase transitions and variable surface tension,
    Recent Developments of Mathematical Fluid Mechanics, 411-442, Birkhäuser, Basel, 2016, (Link to preprint version), (with J. Prüss, S. Shimizu, G. Simonett).

18. Well-posedness and long-time behaviour for the Westervelt equation with absorbing boundary conditions of order zero,
    Journal of Evolution Equations 17, 551-571, 2017 (Link to preprint version), (with G. Simonett).

19. Reaction-diffusion systems of Maxwell-Stefan type with reversible mass-action kinetics,
    Nonlinear Analysis TMA 159, 264-284, 2017 (Link to preprint version), (with M. Herberg, M. Meyries, J. Prüss).
    

20. Stability of Equilibrium Shapes in Some Free Boundary Problems Involving Fluids,
    Handbook of Mathematical Analysis of Viscous Fluids, 2017, Article (Link to preprint version), (with G. Simonett).
    

21. Addendum to the paper “On quasilinear parabolic evolution equations in weighted Lp-spaces II”,
    Journal of Evolution Equations 17, 1381-1388, 2017, Article (Link to preprint version), (with J. Prüss).
    

    
    
22. On critical spaces for the Navier-Stokes equations,
    Journal of Mathematical Fluid Mechanics 20, 733-755, 2018, Article (Link to preprint version), (with J. Prüss).
    
    
23. Critical spaces for quasilinear parabolic evolution equations and applications,
    Journal of Differential Equations 264, 2028-2074, 2018, Article (Link to preprint version), (with J. Prüss, G. Simonett)
    
    
24. The Rayleigh-Taylor instability for the Verigin problem with and without phase transition,
    Nonlinear Differential Equations and Applications (2019) 26: 18. Article  (Link to preprint version)
    (with J. Prüss, G. Simonett)
    
    
25. The two-phase Navier-Stokes equations with surface tension in cylindrical domains,
    Pure and Applied Functional Analysis 5, 121-201, 2020, Article (Link to preprint version)
    
    
26. Well-Posedness and qualitative behaviour of the Mullins-Sekerka problem with ninety-degree angle boundary contact,
    Mathematische Annalen 381, 363-403, 2021, Article (Link to preprint version) (with H. Abels, M. Rauchecker)
    
    
27. On the Navier-Stokes equations on surfaces,
    Journal of Evolution Equations 21, 3153-3179, 2021, Article (Link to preprint version) (with J. Prüss, G. Simonett)
    
    
28. On the Rayleigh-Taylor instability for the two-phase Navier-Stokes equations in cylindrical domains,
    Interfaces and Free Boundaries, 2022. https://doi.org/10.4171/ifb/480
    
    
29. H-infinity calculus for the surface Stokes operator and applications,
    Journal of Mathematical Fluid Mechanics 24, 109, 2022. https://doi.org/10.1007/s00021-022-00742-y (with G. Simonett)
    

Preprints:

1.  Lp-Lq-theory for a quasilinear non-isothermal Westervelt equation,
   submitted for publication, (Link to preprint version) 2022.
   

A short curriculum vitae

Last modified:  October 26, 2022
© Mathias Wilke