L.A. Peletier

Contact information

Phone: +31-71-527.7141
E-mail: peletier@math.LeidenUniv.nl
Office: 203b
Fax: +31-71-527.7101

Courses

Pre-University College

Current projects

1. Nonlinear ordinary and partial differential equations arising in the applied sciences. Special focus on nonlinear diffusion processes and higher order model equations, such as the Swift-Hohenberg equation.

2. Quantitive modelling of pharmaceutical processes.

3. Modelling auxin transport in Arabidopsis plant stems. For details see the "Plant Biodynamcs Lab"

Recent papers


Mathematical:

G.J.B. van den Berg. L.A. Peletier  and W.C. Troy (2001)  Global branches of multi bump periodic solutions of the Swift-Hohenberg equation,  Arch. Rational Mech. Anal. Vol. 158, 91-153.

U. Ebert, W. van Saarloos, and L. A. Peletier (2002), Universal algebraic convergence in time of pulled fronts: the common mechanism for difference-differerential and partial differential equations, Eur. J.  Appl. Math. Vol. 13, 53-66.

D. Hilhorst, L.A. Peletier and R. Schaetzle (2002), Gamma-Limit for the Extended Fisher-Kolmogorov equation, Proc. Royal Soc. Edinburgh, Vol. 132A, 141-162.
L. A. Peletier and Vivi Rottschafer (2002),  Large time behaviour of solutions of the Swift-Hohenberg equation,Comptes Rendu Mathematique, Vol. 336,  225-230


Filippo Gazzola, Bert Peletier, Patrizia Pucci and James Serrin (2003) , Asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters, Part II, Ann. I. H. Poincare, AN Vol. 20, 947-974.

Julia V. Chaparova, Lambertus A. Peletier and Stepan Tersian (2003), Existence and nonexistence of nontrivial solutions of fourth and sixth order ordinary differential equations,  Advances in Differential equations, Vol. 8, 1237-1258.

Julia V. Chaparova, Lambertus A. Peletier and Stepan Tersian (2003), Existence and nonexistence of nontrivial solutions of sixth order ordinary differential equations,  To appear in Applied Mathematics Letters.

R. Kuske & L.A. Peletier (2005), A singular perturbation theorem for a fourth order ordinary differential equation Nonlinearity, Vol. 18, 1189-1222.

L. A. Peletier and Vivi Rottschafer (2004), Pattern selection of solutions of the Swift-Hohenberg equation, Physica D, Vol. 194, 95-126.

 D. Hilhorst, L.A. Peletier, A.I. Rotariu and  G. Sivashinsky (2004), Global Attractor and Inertial Sets for a Nonlocal Kuramoto-Sivashinsky Equation, J. Discrete and Continuous Dynamical Systems, Vol 10, 557-580.

Lambertus A. Peletier and Jose Antonio Rodriguez (2004), Homoclinic orbits to a saddle-center in a fourth order differential equations, J. Differential Equations, Vol. 203, 185-215.

Lambertus A. Peletier and Jose Antonio Rodriguez (2004), Fronts on a lattice, Differential and Integral Equations, Vol. 17, 1013-1042.

H. Brezis and L.A. Peletier  (2004), Elliptic equations with critical exponent on $S^3$: new non-minimising solutions,  C.R. Acad. Sci. Paris, Ser 1. Vol. 339, 391-394.

Lambertus A. Peletier and Jose Antonio Rodriguez (2004), The discrete Swift-Hohenberg equation, Report Mathematical Institute, Leiden University, MI 2004-07.

H. Brezis and L.A. Peletier  (2006), Elliptic equations with critical exponent on spherical caps of $S^3$;   J. d' Analyse Mathematique Vol 98 279-316.

L.A. Peletier and J.F. Williams   (2006), Some canonical bifurcations in the Swift-Hohenberg equation; SIAM Appl. J. Dyn. Syst, Vol. 6, 208-235.

A. Doelman, T. Kaper and L.A. Peletier   (2006), Homoclinic orbits at the onset of pulse self-replication; J. Diff. Equ, Vol. 231, 359-423.

L.A. Peletier   (2006), Nonlinear eigenvalue problems for higher-order model equations; Handbook of Differential Equations, Stationary Partial Differential Equations, Volume 3, Chapter 7, Ed. M. Chipot and P. Quittner, Elsevier.

M.A. Efendiev and L.A. Peletier  (2007), On the large time behavior of solutions of fourth order parabolic equations and $\varepsilon$-entropy of their attractors,   C.R. Acad. Sci. Paris, Ser 1. Vol. 344, 93-96.

C.J. van Duijn, L.A. Peletier and I.S. Pop (2007), A new class of entropy solutions of the Buckley-Leverett equation, SIAM J. Math. Anal. Vol. 39, 507-536.


Pharmaceutical:

K.P. Zuideveld, H.J. Maas, N. Treijtel, J. Hulshof, P.H. van der Graaf, L.A. Peletier and M. Danhof (2001) , A set-point model with oscillatory behavior predicts the time-course of 8-OH-DPAT induced hypothermia, Am J Physiol Regulatory Comp Physiol, Vol. 281,"R2059-2071.

K.P. Zuideveld, L.A. Peletier and M. Danhof (2001),  Of medicine and math, Nieuw Archief voor Wiskunde,Vol. 5, 218-222.

K.P. Zuideveld, N. Treijtel, H.J. Maas, P.H. van der Graaf, L.A. Peletier and M. Danhof (2002), A competitive interaction model predicts the effect of WAY-100,635 on the time course R-(+)-8-Hydroxy-2- (di-n-propylamino) tetralin-induced hypothermia, The Journal of Pharmacology and Experimental Therapeutics (JPET), Vol. 300,  330-338

Klaas P. Zuideveld, Aukje van Gestel,  Piet Hein van der Graaf, Lambertus A. Peletier and Meindert  Danhof (2002),
Pharmacokinetic-pharmacodynamic modelling of the hypothermic and corticosterone effects of the 5-HT_1A receptor agonist flesinoxan, European Journal of Pharmacology, Vol.  445, 43-54.

S.A.G Visser, W.W.F.T. Gladdines, P.H. van der Graaf, L.A. Peletier and M. Danhof (2002), Neuroactive steriodsdiffer in potency but not in intrinsic efficacy in the GABA_A receptor in vivo, The Journal of Pharmacology and Experimental Therapeutics (JPET), Vol. 303,  616-626.

S.A.G Visser, F.L.C. Wolters, J.M. Gubbens-Stibbe, E. Tukker,  P.H. van der Graaf, L.A. Peletier and M. Danhof (2003), Mechanism-based Pharmacokinetic/Pharmacodynamic modeling of the electroencephalogram effects of GABA_A receptor modulators: in vitro-in vivi modulators, The Journal of Pharmacology and Experimental Therapeutics (JPET), Vol. 304, 88-101.

L.A. Peletier (2004), Ordinary Differential Equations in Pharmacodynamics, Report Mathematical Institute, Leiden University, MI 2004-10.

Lambertus A. Peletier, Johan Gabrielsson and Jacintha den Haag (2005), A Dynamical Systems Analysis of the Indirect Response Model with Special Emphasis on Time to Peak Response, J. Pharmacokinetics and Pharmacodynamics, Vol 32, 607-654.

Björn Sallstrom, Sandra A.G. Visser, Tomas Forsberg, Lambertus A. Peletier, Anne-Christine Ericson and Johan Gabrielsson (2005), A novel pharmacodynamic turnover model capturing asymmetric circadian baselines of body temperature, heart rate and blood pressure in rats: challenges in terms of tolerance and animal handling effects. J. Pharmacokinetics and Pharmacodynamics, Vol 32, 835-859.

Sandra A.G. Visser, Björn Sällström, Tomas Forsberg, Lambertus A. Peletier and Johan Gabrielsson (2006). Modeling drug- and system related changes in body temperature: application to Clometiazole-induced hypotyhermia, long-lasting tolerance developments and circadian rhythm in rats; The Journal of Pharmacology and Experimental Therapeutics (JPET), Vol. 317, 209-219.

Klaas P. Zuideveld, Piet H van der Graaf, Lambertus A. Peletier and Meindert Danhof (2007), Allometric scaling of pharmacodynamic responses: Application to 5-HT_1A. Receptor mediated responses from rat to man. Pharm. Research, Vol. 24, 2031-2039.

Johan Gabrielsson and Lambertus A. Peletier (2007), A nonlinear feedback model for tolerance and rebound; Eur. J. Pharm. Sci. Vol. 32, 85-104.

Johan Gabrielsson and Lambertus A. Peletier (2008), A flexible nonlinear feedback system that captures diverse patterns of adaptation and rebound; The AAPS Journal; Vol 10 (1) 70-83.

Marian Geldof, Jan I. Freijer, Lambertus A. Peletier, Ludy van Beijsterveldt and Meindiert Danhof (2008), Mechanistic model for the acute effect of fluvoxamine on 5-HT and 5-HIAA concentrations in rat frontal cortex; Eur. J. Pharm. Sci. Vol 32, 217-229.

Lambertus A. Peletier, Neil Benson and Piet H. van der Graaf (2009), Impact of plasma-protein binding on receptor occupancy: An analytical description; J. Theoretical Biology Vol 256, 253-262.

Hoai-Minh Nguyen and Lambertus A. Peletier (2009), Monotonicity of time to peak response with respect to drug dose for turnover models; Differential and Intergral Equations Vol 22, 1-26.

Johan Gabrielsson and Lambertus A. Peletier (2009), Nonlinear turnover models for systems with physiological limits; Eur. J. Pharm. Sci. Vol 37, 11-26.

Hoai-Minh Nguyen and Lambertus A. Peletier (2009), Monotonicity of the peak time in turnover models; Comptes Rendus Acad. Sci. Paris, Ser. I Vol 347, 495-500.

Lambertus A. Peletier and Johan Gabrielsson (2009), Dynamics of target-mediated drug disposition; to appear in Eur. J. Pharm. Sci.


Book

L.A. Peletier and W.C. Troy (2001), Spatial Patterns: Higher Order Models in Physics and Mechanics, Birkhäuser, Boston.