2.3. Non-lineair Differential Equations

Papers in journals and proceedings

M.E. AKVELD, J. HULSHOF, Travelling wave solutions of a fourth order semi-linear diffusion equation, Applied Mathematics Letters, 11(3), 115-120 (1998).

C. BANDLE, L.A. PELETIER, Best Sobolev constants and Emden equations for the critical exponent in $S3$, Math. Ann., 313, 83-93 (1999).

A. BAUMGÄRTNER, U. EBERT, L. SCHÄFER, Segment motion in the reptation model of polymer dynamics: I Analytic investigation, J. Stat. Phys., 90, 1325-1373 (1998).

A. BAUMGÄRTNER, U. EBERT, L. SCHÄFER, Segment motion in the reptation model of polymer dynamics: II. Stimulations, J. Stat. Phys., 90, 1375-1400 (1998).

A. BAUMGÄRTNER, U. EBERT, L. SCHÄFER, Reptational dynamics of a polymer chain is stable against kinematic disorder, Eur. Phys. J., B 10, 105-117 (1999).

G.J.B. VAN DEN BERG, Uniqueness of solutions for the extended Fisher-Kolmogorov equation, Computes Rendus Acad. Sci. Paris, Serie I, 326, 447-452 (1998).

C.M. BRAUNER, J. HULSHOF, C. SCHMIDT-LAINE, The saddle point property for focusing selfsimilar solutions in a free boundary problem, Proc. A.M.S., 127, 473-479 (1999).

C.M. BRAUNER, J. HULSHOF, C. SCHMIDT-LAINE, Instabilities, bifurcation and saddle-points in some FBP's in combustion. Free boundary problems: theory and applications, Math. Notes, 409, Chapman Hall/CRC, Boca Raton, FL, USA (1999).

J. BRUINING, F.J. VERMOLEN, P.LJ. ZITHA, Modification of two phase flow properties by adsorbed polymers and gels, SPE, 54737, 299-312 (1999).

C.J. BUDD, G.W. HUNT, M.A. PELETIER, Self-similar fold evolution under prescribed end-shortening, J. Math. Geology, 31, 989-1005 (1999).

S.P. CHEN, J. VAN DE LANGKRUIS, M.S. VOSSENBERG, F.J. VERMOLEN, S. VAN DER ZWAAG, Dissolution of $\beta$ particles in an Al-Mg-Si alloy during DSC runs, Materials Science and Engineering, A272, 250-256 (1999).

E.N. DANCER, D. HILHORST, M. MIMURA, L.A. PELETIER, Spatial segregation limit of a competition-diffusion system, European J. Appl. Math., 10, 97-115, (1999).

A. DOELMAN, R.A. GARDNER, T.A. KAPER, Stability analysis of singular patterns in the 1D Gray-Scott model: A matched asymptotics approach, Physica, Vol. 122 1-4, 1-36 (1999).

A. DOELMAN, V. ROTTSCHÄFER, On the transition from the Ginzburg-Landau equation to the extended Fisher-Kolmogorov equation, Physica, Vol 118 3-4, 261-292 (1998).

A. DOELMAN, R. SCHIELEN, Modulation equations for spatially periodic systems: derivation and solutions, SIAMJ. Appl. Math., Vol. 58 6, 1901-1930 (1998).

C.J. VAN DUIJN, L.A. PELETIER, R.J. SCHOTTING, Brine transport in porous media: Self-similar solutions, Advances in water resources, Vol 22 3, 285 (1999).

U. EBERT, W. VAN SAARLOOS, Universal algebraic relaxation of fronts propagating into an unstable state and implications for moving boundary approximations, Phys. Rev. Lett., 80, 1650-1653 (1998).

B.W. VAN DE FLIERT, R. VAN DER HOUT, Stress-driven diffusion in a drying liquid paint layer, European Journal of Applied Mathematics, 9 (5), 447-462 (1998).

B. FRANCHI, L.A. PELETIER, Ground states for Gaussian curvature type equations, Asymptotic Analysis, 17, 53-70 (1998).

G. GALIANO, M.A. PELETIER, Spatial locialization for a general reaction-diffusion system, Annales de la Faculté des Sciences de l'Université de Toulouse, 7, 419-441, (1998).

I. GOHBERG, M.A. KAASHOEK, A.L. SAKHNOVICH, Psuedo-canonical systems with rational Weyl functions: explicit formulas and applications, J. Diff. Eqns., Vol, 146 2, 375-398 (1998).

S.P. HASTINGS, L.A. PELETIER, On self-similar solutions of the thin film equation when $n = 3$, Differential Integral Equations, 11, 1-22 (1998).

D. HILHORST, R. VAN DER HOUT, L.A. PELETIER, Nonlinear diffusion in the presence of fast reaction, Nonlinear Analysis, (1999).

J. HULSHOF, J.R. KING, Analysis of a Darcy flow model with a dynamic pressure saturation relation, SIAM Journal of Applied Math., 59(1), 318-346 (1998).

J. HULSHOF, J.R. KING, Analysis of a Darcy flow model with a dynamic pressure saturation relation, SIAM J. Appl. Math., 59, no 1. 318-346, (1999).

J. HULSHOF, J.R. KING, Asymptotic analysis of an elliptic-parabolic moving boundary problem, Appl. Math. Letters, 12, 87-94 (1999).

J. HULSHOF, E. MITIDIERI, R.C.A.M. VAN DER VORST, Strongly indefinite systems with critical Sobolev exponents, Transactions AMS, 350, 2349-2365 (1998).

J. HULSHOF, A.E. SHISHKOV, The finite speed of propagation property for the thin film equation in terms of the $L1$-norm, Advances in Differential Equations, 3(5), 625-642 (1998).

T. LACHAND-ROVERT, M.A. PELETIER, Extremal points of a functional on the set of convex functions, Proc. A.M.S., 127, 1723-1727 (1999).

V. MIZEL, L.A. PELETIER, W.C. TROY, Periodic phases in second order material, Archive Rational Mechanics Analysis, 145, 343-382 (1998).

L.A. PELETIER, S.I. POKHOZHAEV, The Cauchy problem for the extended Fisher-Kolmogorov equation, Russian Differ. Uravn., 35, 351-366 (1999).

L.A. PELETIER A.I. ROTARTIU-BRUMA, W.C. TROY, Pulse-like spatial patterns described by higher order equations, Journal of Differential Equations, 150, 124-187 (1998).

L.A. PELETIER, W.C. TROY, Multi-bump periodic travelling waves in suspension bridges, Proceedings of the Royal Society of Edinburgh, 128A, 631-659 (1998).

M.A. PELETIER, Non-existence and uniqueness results for fourth-order Hamiltonian systems, Nonlinearity, Vol. 12, 1555-1570 (1999).

F.J. VERMOLEN, C. VUIK, A vector-valued Stefan problem from aluminium industry, NAW, 4, 17, 205-217 (1999).

F.J. VERMOLEN, C. VUIK, S. VAN DER ZWAAG, An asymptotic solution for the dissolution of particles in multi-component alloys, In: Proceedings from Workshop on `Phase change with convection modelling and validation', Warsaw (1999) 155-159.

Reports and pre-prints

H.W. ALT, C.J. VAN DUIJN, A free boundary problem involving a cusp: breakthrough of salt water, CWI report MAS-R9817, (1998).

G.J.B. VAN DEN BERG, The phase-plane picture for a class of fourth-order conservative differential equations, Leiden University W98-23.

G.J.B. VAN DEN BERG, W.D. KALIES, J. KWAPISZ, R.C.A.M. VAN DER VORST, Homotopy classes for stable periodic and chaotic patterns in fourth-order Hamiltonian systems, Leiden University MI 99-11.

G.J.B. VAN DEN BERG, J. HULSHOF, R.C.A.M. VAN DER VORST, Travelling waves for fourth-order semilinear parabolic equations, Leiden University MI 99-16.

G.J.B. VAN DEN BERG, L.A. PELETIER, W.C. TROY, Global branches of multi-bump periodic solutions of the Swift-Hohenberg equation, Leiden University MI 99-17.

F. BERNIS, J. HULSHOF, J.R. KING, Dipoles and similarity solutions of the thin film equation in the half-line, Leiden University, MI 99-10, to appear in Nonlinearity , 13, 2000.

F. BERNIS, J. HULSHOF, F. QUIROS, The linear limit of thin film flows as an obstacle-free boundary problem, Leiden University MI 99-24.

M. BOWEN, J.R. HULSHOF, J.R. KING, Intermediate asymptotics of the porous medium equation with sign changes, Leiden University W98-06.

M. BOWEN, J.R. KING, Moving boundary problems and non-uniqueness for the thin film equation, Leiden University MI 99-28.

M. BOWEN, J.R. KING, Asymptotic behaviour of the thin film equation in bounded domains, Leiden University MI 99-29.

C.M. BRAUNER, J. HULSHOF, A. LUNARDI, A general approach to stability in free boundary problems, Leiden University W98-29.

J. BRUINING, C.J. VAN DUIJN, Uniqueness conditions in a hyperbolic model for oil recovery by steamdrive, CWI report MAS-R9803, (1998).

J. BRUINING, C.J. VAN DUIJN, F.J. VERMOLEN, Gel placement in porous media, Part I: Constant injection rate., CWI report MAS-R9928.

J. BRUINING, G.J. PIETERS, F.J. VERMOLEN, P.L.J. ZITHA, A mathematical model for preflush treatment in an oil reservoir usin a fully miscible fluid, CWI report MAS-R9929, (1999).

S. CLAUDI, L.A. PELETIER, R. TESEI, A free boundary problem involving convection and singular absorption, Leiden University MI 99-13.

C. CUESTA, C.J. VAN DUIJN, J. HULSHOF, Infiltration in Porous Media with Dynamic Capillary Pressure: Travelling Waves, CWI Preprint, (1999).

U. EBERT, W. VAN SAARLOOS, Front propagation into unstable states: universal algebraic convergence towards uniformly translating pulled fronts, CWI report MAS-R9908.

B.W. VAN DE FLIERT, R. VAN DER HOUT, A nonlinear Stefan problem with negative latent heat, arising in a diffusion model, Leiden University W98-11.

J.K. HALE, L.A. PELETIER, W.C. TROY, Exact homoclinic and heteroclinic solutions of the Gray-Scott model for autocatalysis, Report of the Center for Dynamical Systems and Nonlinear Studies, Georgia Tech (1998).

D. HILHORST, L.A. PELETIER, I.A. ROTARIU-BRUMA, G. SIVASHINSKY, Global attractor and inertial sets for a nonlocal Kuramoto-Sivashinsky equation, Leiden University MI 99-06.

R. VAN DER HOUT, Singularities and nonuniqueness in cylindrical flow of nematic liquid crystals, Leiden University MI 99-20.

R. VAN DER HOUT, Draw resonance in isothermal fiber spinning of Newtonian and power law fluids, Leiden University, MI 99-21 (to appear in EJAM).

G.W. HUNT, M.A. PELETIER, M.A. WADEE, The Maxwell stability criterion in pseudo-energy models of kinks banding, CWI report MAS-R9911, (1999).

T. LACHAND-ROBERT, M.A. PELETIER, An example of non-convex minimization and an application to Newton's problem of the body of least resistance, CWI report MAS-R9912, (1999).

M.A. PELETIER, Sequential buckling: A variational analysis, CWI report MAS-R9920, (1999).

M.A. PELETIER, Non-existence and uniqueness results for the extended Fisher-Kolmogorov equation, CWI report MAS-R9903, (1999).

A. SEGAL, F.J. VERMOLEN, C. VUIK, A conserving discretisation for the free boundary in a two-dimensional Stefan-problem with a kinetic boundary condition, CWI report MAS-R9904, (1999).

F.J. VERMOLEN, C. VUIK, A mathematical model for the dissolution of particles in multi-component alloys, CWI report MAS-R9822, (1998).