2.3. Non-lineair Partial Differential Equations

Papers in journals and proceedings

E. BERETTA, J. HULSHOF & L.A. PELETIER, On an ODE from forced coating flow, Diff. Eqns. 130 (1996), 247-265.

F. BERNIS & L.A. PELETIER, Two problems from draining flows involving third-order ordinary differential equations, SIAM, J. Math. Anal. 27 (1996) 515-527.

PH. CLfEMENT, P. FELMER AND E. MITIDIERI, Solutions homoclines d'un système hamiltonien non-borné et superquadratique, C.R. Acad. Sci. Paris, tome 320, (1995), 1481-1484.

PH. CLfEMENT, D.G. DE FIGUEIREDO AND E. MITIDIERI, A Priori estimates for positive solutions of semilinear elliptic systems via Hardy-Sobolev inequalities, in Nonlinear partial differential equations, Pitman Res. Notes Math. Ser. 343, Longman Sci. Tech. Harlow (1996), 73-91.

PH. CLfEMENT, D.G. DE FIGUEIREDO AND E. MITIDIERI, Quasilinear elliptic equations with critical exponent, Topological Methods in Nonlinear Analysis, 7, (1996), 133-170.

PH. CL´EMENT, R. HAGMEIJER, G. SWEERS, On a Dirichlet problem related to the invertibility of mappings arising in 2D grid generation problems, in: Calculus of variations, applications and computations, Pont-à-Mousson 1994, (ed. C. Bandle, J. Bemelmans, and M. Chipot) Pitman Research Notes in Math. 326, Longman, Harlow (1995), 67-83.

PH. CL´EMENT, R. HAGMEIJER & G. SWEERS, On the invertibility of mappings arising in 2D grid generation problems, Numer. Math., 73, (1996), 37-51.

PH. CL´EMENT, R. MAN´ASEVICH & E. MITIDIERI, On a modified capillary equation, J. Diff. Equations, 124, (1996), 343-358.

PH. CLfEMENT R.C.A.M. VAN DER VORST, On a semilinear elliptic system, Differential and Integral Eq., 8, (1995), 1317-1329.

P.R. DEN DECKER, R. VAN DER HOUT, C.J. VAN DUIJN & L.A. PELETIER, A Stefan problem in a Bridgman crystal grower, Euro. J. Appl. Math. 6 (1995), 191-199.

M.I.J. VAN DIJKE, C.J. VAN DUIJN & S.E.A.T.M. VAN DER ZEE, Multiphase flow modeling of air sparaging, Adv. Water Res. 18 (1995) 319-333.

C.J. VAN DUIJN, W.J.P. BOSMA & S.E.A.T.M. VAN DER ZEE, Plume development of a nonlinearly adsorbing solute in heterogeneous porous formations, Water Resources Research 32, (1996), 1569-1584.

C.J. VAN DUIJN, C.N. DAWSON & R.E. GRUNDY, Large time asymptotics in contaminant transport in porous media, SIAM Appl. Math. 56, (1996), 965-993.

C.J. VAN DUIJN, & F.J.T. FLORIS, On a singular diffusion equation originating from porous media flow, Asymp. Anal. 10 (1995), 29-48.

C.J. VAN DUIJN, S. HENGST & P. KNABNER, An analysis of crystal dissolution fronts in flows through porous media, Part I: Compatatible boundary conditions, Adv. Water Res. 18 (1995), 171-185.

C.J. VAN DUIJN & C.A. MILLER, Similarity solutions for gravity-dominated spreading of a lens of organic contaminant, In: M.F. Wheeler, Environmental Studies: Mathematical, Computational and Statistical Analysis, pp. 291-304, IMA Volumes in Mathematics and its Applications, Springer Verlag (1996).

C.J. VAN DUIJN, J. MOLENAAR & M.J. DE NEEF, The effect of capillary forces on immiscible two-phase flow in heterogeneous porous media, Trans. Porous Media 21 (1995), 71-93.

C.J. VAN DUIJN & M.A. PELETIER, Asymptotic behaviour of solutions of a nonlinear transport equation, Jour. für die reine und angew. Math (1996).

C.J. VAN DUIJN, & P.A.C. RAATS, A note on horizontal distribution with capillary hysteresis, Water Resources Res. 17 (1995), 61-83.

P.C. FIFE & L.A. PELETIER, On the location of defects in stationary solutions of the Ginzburg-Landau equation in , Quart. Appl. Math. 54 (1996), 85-104.

B.W. VAN DER FLIERT, The viscous modulation of Lamb's dipole vortex, Phys. Fluids, 8 (1996), 1975-1977.

B.W. VAN DER FLIERT, Planar relative equilibrium vortices with free boundaries, Nonlinearity 8 (1995), 963-982.

H.-CH. GRUNAU, G. SWEERS, Classical solutions for some higher order semilinear elliptic equations under weak growth conditions, Nonlinear Analysis, T.M.A. 28 (1997), 799-807.

H.-CH. GRUNAU, G. SWEERS, Positivity for perturbations of polyharmonic operators with Dirichlet boundary conditions in two dimensions, Math.Nachrichten. 179 (1996), 89-102.

D. HILHORST, R. VAN DER HOUT & L.A. PELETIER, The fast reaction limit for a reaction-diffusion system, J. Math. Anal. Appl. 199 (1996), 349-373.

J. HULSHOF, A local analysis of similarity solutions of the thin film equation, Gakuto International Series, Mathematical Sciences and Applications 7 (1995), 179-192.

J. HULSHOF & J.L. VAZQUEZ, Maximal viscosity solutions of the modified porous medium equation and their asymptotic behaviour, Euro. J. App. Math. 7 (1996), 453-471.

J. HULSHOF & R.C.A.M. VAN DER VORST, Asymptotic behaviour of ground states, Proc. A.M.S. Vol 124, 8 (1996), 2423-2431.

J.F. KAASHOEK AND JEAN H.P. PAELINCK, Studying the Dynamics of Pre-Geographical Space by Means of Space and Time-Potential Partial Differential Equations, Geographical Systems, 1996, Vol. 2, pp. 83-101

W.D. KALIES & C.A.M. VAN DER VORST, Countable families of homoclinic and heteroclinic connections for the extended Fisher-Kolmogorov equation, Journ. Diff. Eq. 131 (1996), 209-228.

E. MITIDIERI, G. SWEERS, Weakly coupled systems and positivity, Math. Nachrichten 173 (1995), 259-286.

E. MITIDIERI, G. SWEERS, R.C.A.M. VAN DER VORST, Non existence theorems for systems of quasilinear partial differential equations, Differential and Integral Equations 8 (1995), 1331-1354.

A. DEN OUTER, J.F. KAASHOEK AND H.R.G.K. HACK, Difficulties with using continuous fractal theory for discontinuity surfaces, Int. J. Rock Mech. Min. Sci. & Geomech., Vol.32, No. 1, pp. 3 - 9, 1995.

A. DEN OUTER, J.F. KAASHOEK AND H.R.G.K. HACK Discussion on using continuous fractal theory, Int. J. Rock Mech. Min. Sci. & Geomech., Vol. 33, No. 4, pp. 439-442, 1996.

L.A. PELETIER & H. SERAFINI, A very singular solution and other self-similar solutions of the heat equation with convection, Nonlinear Anal. T.M.A. 24 (1995), 29-49.

L.A. PELETIER & W.C TROY, Spatial patterns described by the extended Fisher-Kolmorogov (EFK) equation: Kinks, Diff. Int. Eqns. 8 (1995) 1279-1304.

L.A. PELETIER & W.C. TROY, Self-similar solutions for a free boundary problem in the doping of semiconductors, Eur. J. Appl. Math. 6 (1995) 169-189.

L.A. PELETIER & W.C. TROY, Chaotic spatial patterns described by the EFK equation, J. Diff. Eqns. 126 (1996), 458-508.

L.A. PELETIER & W.C. TROY, Spatial patterns in higher order phase transitions, CWI Quart. 1 2 (1996), 121-129.

L.A. PELETIER & W.C. TROY, A topological shooting method and the existence of kinks in the Extended Fisher-Kolmogorov equation, Topol. Methods in Nonlinear Anal. 6 (1996) 331-355.

L.A. PELETIER, W.C. TROY & R.C.A.M. VAN DER VORST, Stationary solutions of a fourth order nonlinear diffusion equation, (In Russian), Diff. Eqns. 31 (1995), 327-337.

R.C.A.M. VAN DER VORST, Fourth order elliptic equations with critical growth, C.R. Acad. Sci. Paris, 320 (I) (1995), 295-299.

Reports and pre-prints

M. AKVELD & J. HULSHOF, Travelling wave solutions of a 4th order semilinear diffusion equation, Leiden University, W96-22, to appear in Appl. Math. Letters.

PH. CLfEMENT, P. FELMER AND E. MITIDIERI, Homoclinic orbits for a class of infinite dimensional Hamiltonian systems, to appear in Ann. Scuola Norm. Sup. Pisa.

PH. CLfEMENT, R. MANfASEVICH AND E. MITIDIERI, Some Existence and Non-existence Results for a Homogeneous Quasilinear Problem, to appear in Asymptotic Analysis.

PH. CLfEMENT, R.C.A.M. VAN DER VORST, On the non-existence of homoclinic orbits for a class of infinite dimensional Hamiltonian systems, to appear in Proc. A.M.S.

C.J. VAN DUIJN, C.N. DAWSON & R.E. GRUNDY, Limiting profiles in reactive solute transport, report AM-R9604 (March 1996), to appear in Transport in Porous Media.

C.J. VAN DUIJN & M.J. DE NEEF, Self-similar profiles for capillary diffusion driven flow in heterogeneous porous media, report AM-R9601 (January 1996), to appear in Advances in Water Resources.

C.J. VAN DUIJN & J.R. PHILIP, Slumping of Brine Mounds: Bounds on Behavior, accepted for publication in Journal of Hydrology 179, (1996), 159-180.

C.J. VAN DUIJN & R.J. SCHOTTING, Brine transport in porous media: self-similar solutions, report AM-R9616 (November 1996).

C.J. VAN DUIJN, R.J. SCHOTTING & P. KNABNER, An analysis of crystal dissolution fronts in flows through porous media. Part II: Incompatible boundary conditions, report AM-R9609 (July 1996), to appear in Advances in Water Resources.

P. FREITAS, G. SWEERS, Positivity results for a nonlocal elliptic equation, preprint.

V.A. GALAKTIONOV, J. HULSHOF & J.L. VAZQUEZ, Extinction and focusing behaviour of spherical and annular flames described by a free boundary problem, Leiden University, W96-10, to appear in J. Math. Pures & Appl.

V.A. GALAKTIONOV & L.A. PELETIER, Aysmptotic behaviour near finite time extinction for the fast diffusion equation, Leiden University W95-11, to appear in Arch. Rational Mech. Anal.

H.-CH. GRUNAU, G. SWEERS, Positivity for equations involving polyharmonic elliptic operators with Dirichlet boundary conditions, to appear in Mathematische Annalen.

H.-CH. GRUNAU, G. SWEERS, The maximum principle and positive principal eigenfunctions for polyharmonic equations, preprint.

H.-CH. GRUNAU, G. SWEERS, Positivity properties of elliptic Dirichlet problems of higher order, to appear in Proceedings WCNA96, Elsevier Science LTD.

S.P. HASTINGS & L.A. PELETIER, On self-similar solutions of the thin film equation when n = 3, Leiden University, W96-08, to appear in Diff. Int. Eqns.

D. HILHORST, R. VAN DEN HOUT & L.A. PELETIER, Diffusion in the presence of fast reaction: the case of the general monotone reaction term, Leiden University, W96-01. To appear in J. Math. Sci. Tokyo.

J. HULSHOF, E. MITIDIERI & R.C.A.M. VAN DER VORST, Strongly indefinite system with critical Sobolev exponents, Leiden University, W95-15, to appear in Trans. A.M.S.

J. HULSHOF & J.R. KING, Analysis of a Darcy flow model with a dynamic pressure saturation relation, Leiden University, W96-14, to appear in SIAM J. Appl. Math.

J.F. KAASHOEK AND J.H.P. PAELINCK, Studying the Dynamics of Pre-Geographical Space by Means of Space and Time-Potentialised Partial Differential Equations, pp. 1-23, Report 9538/A, Ecometric Institute, Erasmus University Rotterdam, 1995

J.F. KAASHOEK AND J.H.P. PAELINCK, Potentialised Partial Differential Equations in Economic Geography and Spatial Economics: Multiple Dimensions and Control, (pp. 1-25) Report 9664/B Econometric Institute.

W. D. KALIES, J. KWAPISZ & R.C.A.M. VAN DER VORST, Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria, to appear in Comm. Math. Phys.

W.D. KALIES, R.C.A.M. VAN DER VORST & T. WANNER, Slow motion in higher-order systems and -convergence in one space dimension, preprint CDSNS 1996.

S. LI AND G. SWEERS, Closed-form solution for a moving boundary problem.

R. MANfASEVICH, G. SWEERS, A noncooperative system with p-Laplacians that preserves positivity, report 95-84 TWI, TUDelft.

L.A. PELETIER & S.I. POHOZAEV, The Cauchy problem for the extended Fisher-Kolmorogov (EFK) equation, Leiden University, W96-07.

L.A. PELETIER & W.C. TROY, Spatial patterns described by the Extended Fisher-Kolmogorov (EFK) equation: Periodic solutions, IMA Preprint Series # 1289, February 1995, to appear in SIAM J. Math. Anal.

L.A. PELETIER & W.C. TROY, Multibump periodic travelling waves in suspension bridges, Leiden University, W96-17, to appear in Proc. Roy. Soc. Edinburgh.

N. STAVRAKAKIS, G. SWEERS, Positivity for a noncooperative system of elliptic equations in , report 96-15 TWI, TUDelft.

G. SWEERS, Hopf's lemma and two-dimensional domains with corners, report 96-46 TWI, TUDelft.

G. SWEERS, is sharp for the antimaximum principle, to appear in J. Diff. Equ.