Nonlinear free boundary problems: propagation and regularity

Project title: Nonlinear free boundary problems: propagation and regularity

Principal investigator: Dr Maolin Zhou (UNE)

Funding body:   Australian Research Council (2017-2020)

Project description:
Nonlinear free boundary problems arise from many applied fields, and pose great challenges to the theory of nonlinear partial differential equations, as the underlying domain of the solution to such problems has to be solved together with the solution itself. This project aims to completely understand the propagation profile and regularity of two important classes of free boundary problems, which would greatly enhance the existing theory of partial differential equations, and extend its applications to situations not covered before.

Related publications:

  1. Y.Du, B.Lou and M.Zhou, Spreading and vanishing for nonlinear Stefan problems in high space dimensions, J. Elliptic and Parabolic Equations, 2 (2016), 297-321.
  2. Y.Du, M.Wang and M.Zhou, Semi-wave and spreading speed for the diffusive competition model with a free boundary, J. Math. Pures Appl. (9) 107(2017), 253-287.
  3. W.Lei, G.Zhang and M.Zhou, Long time behavior for solutions of the diffusive logistic equation with advection and free boundary, Calculus of Variations and PDEs 55 (2016), no. 4, 1-34.
  4. X.Chen, B.Lou, M.Zhou and T.Giletti, Long time behavior of solutions of a reaction diffusion equation on unbounded intervals with Robin boundary conditions, Ann. Inst. H. Poincare Anal. Non Lineaire 33 (2016), no. 1, 67-92.
  5. H.Gu, B.Lou and M.Zhou, Long time behavior of solutions of Fisher-KPP equation with advection and free boundaries,  J. Funct. Anal. 269 (2015), no. 6, 1714-1768.
  6. T.Giletti, L.Monsaingeo and M.Zhou, A KPP road-field system with spatially periodic exchange terms, Nonlinear Anal. 128 (2015), 273-302.
  7. Y.Du, B.Lou and M.Zhou, Nonlinear diffusion problems with free boundaryes: convergence, transition speed and zero number arguments, SIAM J. Math. Anal. 47 (2015), no. 5, 3555-3584.
  8. Y.Du, H.Matsuzawa and M.Zhou, Spreading speed and profile for nonlinear Stefan problems in high space dimensions, J. Math. Pures Appl. (9) 103 (2015), no. 3, 741-787.
  9. J.Cai, B.Lou and M.Zhou, Asymptotic behavior of solutions of a reaction diffusion equation with free boundary conditions, J. Dynam. Differential Equations 26 (2014), no. 4, 1007-1028.
  10. Y.Du, H.Matsuzawa and M.Zhou, Sharp estimate of the spreading speed determined by nonlinear free boundary problems, SIAM J. Math. Anal. 46 (2014), no. 1, 375-396.