# J. Hulshof

## Publications

For numbers 60 and higher see MathSciNet and google scholar for journal references. Search for both Joost and Josephus Hulshof to find recent work. For instance on metabolic states.

1. Amplitude saturation of MEMS resonators explained by autoparametric resonance,
C van der Avoort, R van der Hout, J J M Bontemps, P G Steeneken, K Le Phan, R H B Fey, J Hulshof and J T M van Beek,
2. Parametric resonance and Hopf bifurcation analysis for a MEMS resonator,
Cas van der Avoort, Josephus Hulshof, Rein van der Hout.
3. Existence and linear stability of solutions of the ballistic VSC model,
J. Hulshof, R. Nolet, G. Prokert, CASA-Report 09-33.
4. How Hepatitis D Virus Can Hinder the Control of Hepatitis B Virus,
Maria Xiridou, Barbara Borkent-Raven, Joost Hulshof, Jacco Wallinga.
5. A fully nonlinear equation for the flame front in a quasi-steady combustion model,
with Claude-Michel Brauner, Luca Lorenzi and Grisha Sivashinsky, submitted (2009).
6. Energy concentration for 2-dimensional radially symmetric equivariant harmonic map heat flows,
with Michiel Bertsch en Rein van der Hout, submitted (2009).
7. Stability of the Travelling Wave in a 2D Weakly Nonlinear Stefan Problem,
with Claude-Michel Brauner and Luca Lorenzi, submitted (2008).
8. On the kappa-theta model of cellular flames, existence in the large and asymptotics,
Brauner, Frankel, Hulshof, Lunardi and Sivashinsky, to appear in DCDS-S.
9. The radius of vanishing bubbles in equivariant harmonic map flow from $D^2$ to $S^2$,
Sigurd Angenent, Joost Hulshof and Hiroshi Matano.
10. Veranderingen,
Nieuw Archief voor de Wiskunde, 5/7 nr1. (2006).
11. Flame balls for a free boundary combustion problem with radiative transfer,
with JanBouwe van den Berg and Vincent Guyonne.
12. Stability and Attractor for Quasi-Steady Equation of Cellular Flames,
Claude-Michel Brauner, Michael Frankel, Josephus Hulshof and Victor Roytbird (Bordeaux preprint).
13. The speed law for highly radiative flames in a gaseous mixture with large activation energy,
JanBouwe van den Berg, Claude-Michel Brauner, Josephus Hulshof and Alessandra Lunardi,
SIAM J. Appl. Math. 66 (2005) nr. 2, 408-432 (ps file).
14. Weakly nonlinear asymptotics of the kappa-theta model for cellular flames,
Claude-Michel Brauner, Michael Frankel, Josephus Hulshof and Grisha Sivashinsky,
Interfaces and Free Boundaries 7 (2005), nr 2, 131-146.
15. Singularities at $t=\infty$ in Equivariant Harmonic Map Flow ,
Sigurd B. Angenent and Joost Hulshof, Contemp. Math. 367 (2005), 1-15.
16. Stability in a two-dimensional combustion model,
with Luca Lorenzi,
Interfaces and Free Boundaries 6 (2004) nr. 1, 1-29.
17. Nieuwe dimensies, ruimer bereik,
NAW 5/3 2002.
18. Formal asymptotics of bubbling in the harmonic map heat flow,
Jan Bouwe van den Berg, Joost Hulshof and John R. King,
SIAM J. Appl. Math. 63 (2003), no. 5, 1682--1717.
19. Parametric dependence of exponents and eigenvalues in focussing porous media flows (pdf file),
with Donald G. Aronson and Jan Bouwe van den Berg,
European J. Appl. Math. 14 (2003), no. 4, 485--512 (ps file).
20. Multiplicity and stability of travelling wave solutions in a free boundary combustion-radiation problem,
with Olivier Baconneau and Claude-Michel Brauner, revised with Jan Bouwe van den Berg,
EJAM 15 (2004), nr 1, 79-102.
21. A set-point model with oscillatory behavior predicts the time-course of 8-OHDPAT-induced hypothermia,
Klaas P. Zuideveld, Hugo J. Maas, Nicoline Treijtel, me, Piet H. van der Graaf, Bert Peletier en Meindert Danhof,
American Journal of Physiology 281 (2001), 2059--2071,
22. A model problem for groundwater flow with dynamic capillary pressure: stability of travelling waves,
with C. Cuesta,
accepted for publication in Nonl. Anal. TMA.
23. Existence of travelling wave solutions in a combustion-radiation model,
with Claude-Michel Brauner and Jean-Francois Ripoll,
Discrete and Continuous Dynamical Systems 1(2):193-208, 2001.
24. Some aspects of the thin film equation,
Proceedings of European Congress of Mathematics Vol. II,
Progress in Math. Vol 202, 291--301, Birkhauser Verlag 2001.
25. A critical case of stability in a free boundary problem,
with Claude-Michel Brauner and Alessandra Lunardi.
Journal of Evolution Equations 1, 85-113 (2001).
26. Anomalous exponents and dipole solutions for the thin film equation,
with J.R. King and Mark Bowen,
revised version of Leiden preprint MI 01-2000, accepted for publication in SIAM Journal of Applied Math.
27. Infiltration in Porous Media with Dynamic Capillary Pressure: Travelling Waves,
with C.J. van Duijn and C. Cuesta,
CWI-preprint (1999), Eur. J. Appl. Math. 11, 381-397 (2000).
28. The linear" limit of thin film flows as an obstacle-free boundary problem,
with F. Bernis and F. Quiros,
SIAM Journal of Applied Math. 61(3), 1062-1079 (2000).
29. Travelling waves for fourth-order semilinear parabolic equations,
with G.J.B. van den Berg and R.C.A.M van der Vorst,
Leiden preprint MI 16-99 (1999), SIAM J. Math. Anal. 32(6), 1342-1374 (2001) (pdf file).
30. Dipoles and similarity solutions of the thin film equation in the half-line ,
featured article with F. Bernis and J.R. King,
Leiden preprint MI 10-99 (1999), Nonlinearity, 13 (2000), 413-439.
31. A general approach to stability in free boundary problems,
with Claude-Michel Brauner and Alessandra Lunardi,
J. Diff. Equ. 164, 16-48 (2000)
32. Instabilities, bifurcation and saddle-points in some FBP's in combustion,
with Claude-Michel Brauner, Alessandra Lunardi and Claudine Schmidt-Laine,
Leiden preprint W98-10 (1998), appeared in Free boundary problems: theory and applications (Crete, 1997), 105--114, Chapman & Hall/CRC Res. Notes Math., 409, Chapman & Hall/CRC, Boca Raton, FL, 1999.
33. Some transformations related to the Thin Film Equation,
just a small note (1997), accepted for publication on my home page.
34. Asymptotic analysis of an elliptic-parabolic moving boundary problem,
with J.R. King,
Appl. Math. Letters. 12, 87-94 (1999).
35. Intermediate asymptotics of the porous medium equation with sign changes,
with J.R. King and Mark Bowen,
Adv. Diff. Equ. 6(9), 1115-1152 (2001).
36. The saddle point property for focusing selfsimilar solutions in a free boundary problem,
with Claude-Michel Brauner and Claudine Schmidt-Laine,
Proc. A.M.S. 127, 473-479 (1999) (pdf file).
37. The finite speed of propagation property for the thin film equation in terms of the $L^1$-norm,
with Andrey E. Shishkov,
Adv. Diff. Equ. 3(5), 625-642 (1998).
38. Travelling wave solutions of a fourth order semi-linear diffusion equation,
with M.E. Akveld,
Appl. Math. Letters. 11(3), 115-120 (1998).
39. Analysis of a Darcy flow model with a dynamic pressure saturation relation,
with J.R. King,
SIAM Journal of Applied Math. 59(1), 318-346 (1998).
40. Extinction and focusing behaviour of spherical and annular flames described by a free boundary problem,
with Victor A. Galaktionov and J.L. Vazquez,
Journal Math. Pures et Appl. 76, 563-608 (1997).
41. Strongly indefinite systems with critical Sobolev exponents,
with Enzo Mitidieri and R.C.A.M. van der Vorst,
Trans. AMS 350, 2349-2365 (1998) (pdf file).
42. On an ODE from forced coating flow,
with E. Beretta and L.A. Peletier,
J. Diff. Equ. 130(1), 247-265, (1996).
43. Asymptotic Behaviour of Ground States,
with R.C.A.M. van der Vorst,
Proc. A.M.S. 124, 2423-2431, 1996 (pdf file).
44. A local analysis of similarity solutions of the thin film equation,
Gakuto International Series, Mathematical sciences and Applications 7, 179-192, 1995.
45. Maximal viscosity solutions of the modified porous medium equation and their asymptotic behaviour,
with J.L. Vazquez,
Eur. J. Appl. Math. 7, 453-471, 1996.
46. Recent results on selfsimilar solutions of degenerate nonlinear diffusion equations,
Reaction Diffusion Systems (eds. G. Caristi and E. Mitidieri),
Lectures Notes in Pure and Applied Mathematics Vol. 194., Marcel Dekker, 1997.
47. Selfsimilar solutions for the $k-\varepsilon$ model in turbulence,
Leiden preprint W93-11 (1993), "Selfsimilar solutions of Barenblatt's model for turbulence",
SIAM Journal of Math. Anal. 28(1), 33-48, 1997 (pdf file).
48. Selfsimilar solutions of the second kind for the modified porous medium equation,
with J.L. Vazquez,
Eur. J. Appl. Math, 5, 391-403 (1994).
49. A free boundary focusing problem,
with D. Hilhorst,
Proc. A.M.S. 121(4), 1193-1202 (1994).
50. Differential systems with strongly indefinite structure,
with R.C.A.M. van der Vorst,
J. Funct. Anal. 114, 32-58 (1993).
51. Positive solutions of the equation $\Delta u+u^p=$ on a bounded domain,
with R.C.A.M. van der Vorst,
Leiden preprint W93-06 (1993).
52. The dipole solution for the porous medium equation in more space dimensions,
with J.L. Vazquez,
Annali della Scuola Normale Superiore di Pisa Serie IV 20, 193-217 (1993).
53. The semilinear heat equation with a Heaviside source term,
with R. Gianni,
Eur. J. Appl. Math. 3, 367-379 (1992).
54. Spherically symmetric solutions of an elliptic-parabolic Neumann problem,
Rocky Mountain Journal of Mathematics 21(2), 671-681 (1991).
55. A very singular solution for the dual porous medium equation and the asymptotic behaviour of general solutions,
with F. Bernis and J.L. Vazquez,
J. reine angew. Math. 435, 1-31 (1993).
56. On a free boundary problem arising in detonation theory: convergence to travelling waves,
with M. Bertsch and D. Hilhorst,
"Free boundary problems" (eds. J.Chadam & H. Rasmussen.), Pitman (1993).
57. An elliptic-parabolic problem in combustion theory: convergence to travelling waves,
with D. Hilhorst,
J. Nonl. Anal. TMA 16 (1991).
58. The quenching problem on the $N$-dimensional ball,
with M. Fila and P. Quittner,
"Nonlinear diffusion equations" (eds. L.A. Peletier & J. Serrin), Birkhäuser (1992).
59. A note on the quenching rate,
with M. Fila,
Proc. AMS 112, 473-477 (1991).
60. Similarity solutions of the porous media equation with sign changes,
J. Math. Anal. & Appl. 157, 75-111 (1991).
61. Similarity solutions of the porous media equation with sign changes, research announcement,
Appl. Math. Letters. 2(3), 229-232 (1989).
62. Existence of stationary solutions in the coronal loop problem,
with D. Terman and F. Verhulst,
J. Nonl. Anal. TMA 13(7), 841-856 (1989).
63. Monotone flows in N-dimensional partially saturated porous media: Lipschitz continuity of the interface,
with N. Wolanski,
Arch. Rat. Mech. & Anal. 102(4), 287-305 (1988).
64. Bounded weak solutions of an elliptic-parabolic Neumann problem,
Trans. AMS 303(1), 211-227 (1987).
65. Fluid flow in partially saturated porous media,
with M. Bertsch,
in "Semigroups, theory and applications Vol. I" (eds. Brezis, Crandall & Kappel),
Pitman research notes 141, 28-35 (1986).
66. An elliptic-parabolic problem with a nonlocal boundary condition,
with C.J. van Duijn,
Arch. Rat. Mech. & Anal. 99, 61-73 (1987).
67. Regularity results for an elliptic-parabolic Neumann problem,
with M. Bertsch,
Trans. AMS 297, 337-350 (1986).
68. The fluid flow in a partially saturated porous medium: behaviour of the free boundary,
Leiden preprint W85-21 (1985).
69. An elliptic-parabolic free boundary problem: continuity of the free boundary,
Proc. Roy. Soc. Edinb. 106A, 327-339 (1987).
70. An elliptic-parabolic free boundary problem,
with L.A. Peletier,
J. Nonl. Anal. TMA 10, 1327-1346 (1986).
71. The interface in an elliptic-parabolic problem,
with L.A. Peletier.
in "Free boundary problems: applications and theory Vol. III" (eds. Bossavit, Damlamian & Fremond),
Pitman research notes 120, 248-254 (1985).

## Educational/recreational

1. Spectral theory, Stieltjes course notes (2000).
2. Elliptic and Parabolic Equations, course notes (1995).
3. The Heat and the Wave Equation, course notes (1993).
4. Linear Partial Differential Equations, course notes (1993).
5. Metrische ruimten en continue afbeeldingen
6. Handout Functional Analysis 1999
7. Iteraties met de afbeelding van Verhulst
8. De Mandelbrot verzameling (See Bob Devaney's home page, The Mandelbrot/Julia Set Applet, and Mandelbrot Set Explorer).
9. De wortel uit -1, Cardano, Kepler en Newton