Hilhorst, Danielle; Salin, Florian; Schneider, Victor; Gao, Yueyuan Lecture notes on the singular limit of reaction-diffusion systems. (English) Zbl 1526.35027 Interdiscip. Inf. Sci. 29, No. 1, 1-53 (2023). MSC: 35B25 35K51 35K57 92D25 PDFBibTeX XMLCite \textit{D. Hilhorst} et al., Interdiscip. Inf. Sci. 29, No. 1, 1--53 (2023; Zbl 1526.35027) Full Text: DOI
Bertsch, Michiel; Hilhorst, Danielle; Izuhara, Hirofumi; Mimura, Masayasu; Wakasa, Tohru A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic Fisher-KPP equation. (English) Zbl 1435.35126 Discrete Contin. Dyn. Syst. 40, No. 6, 3117-3142 (2020). MSC: 35G55 35A01 35K57 35C07 35K65 92D25 PDFBibTeX XMLCite \textit{M. Bertsch} et al., Discrete Contin. Dyn. Syst. 40, No. 6, 3117--3142 (2020; Zbl 1435.35126) Full Text: DOI
Crooks, E. C. M.; Hilhorst, D. Self-similar fast-reaction limits for reaction-diffusion systems on unbounded domains. (English) Zbl 1375.35254 J. Differ. Equations 261, No. 3, 2210-2250 (2016). MSC: 35K57 35C06 35K51 35M33 35Q92 35R25 92E20 PDFBibTeX XMLCite \textit{E. C. M. Crooks} and \textit{D. Hilhorst}, J. Differ. Equations 261, No. 3, 2210--2250 (2016; Zbl 1375.35254) Full Text: DOI arXiv
Boussaïd, Samira; Hilhorst, Danielle; Nguyen, Thanh Nam Convergence to steady state for the solutions of a nonlocal reaction-diffusion equation. (English) Zbl 1433.35190 Evol. Equ. Control Theory 4, No. 1, 39-59 (2015). MSC: 35K91 35B35 35B40 35K20 35K57 35R09 PDFBibTeX XMLCite \textit{S. Boussaïd} et al., Evol. Equ. Control Theory 4, No. 1, 39--59 (2015; Zbl 1433.35190) Full Text: DOI
Hilhorst, Danielle; Murakawa, Hideki Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium. (English) Zbl 1307.35138 Netw. Heterog. Media 9, No. 4, 669-682 (2014). MSC: 35K51 35K05 35K57 80A22 80A30 35B25 PDFBibTeX XMLCite \textit{D. Hilhorst} and \textit{H. Murakawa}, Netw. Heterog. Media 9, No. 4, 669--682 (2014; Zbl 1307.35138) Full Text: DOI
Hilhorst, Danielle; Rybka, Piotr Stabilization of solutions to a FitzHugh-Nagumo type system. (English) Zbl 1187.82090 J. Stat. Phys. 138, No. 1-3, 291-304 (2010). MSC: 82C26 35K57 37B35 82D60 PDFBibTeX XMLCite \textit{D. Hilhorst} and \textit{P. Rybka}, J. Stat. Phys. 138, No. 1--3, 291--304 (2010; Zbl 1187.82090) Full Text: DOI
Bouillard, N.; Eymard, R.; Henry, M.; Herbin, R.; Hilhorst, D. A fast precipitation and dissolution reaction for a reaction-diffusion system arising in a porous medium. (English) Zbl 1167.35396 Nonlinear Anal., Real World Appl. 10, No. 2, 629-638 (2009). MSC: 35K57 35B45 35K50 76S05 PDFBibTeX XMLCite \textit{N. Bouillard} et al., Nonlinear Anal., Real World Appl. 10, No. 2, 629--638 (2009; Zbl 1167.35396) Full Text: DOI
Hilhorst, D.; van der Hout, R.; Mimura, M.; Ohnishi, I. A mathematical study of the one-dimensional Keller and Rubinow model for Liesegang bands. (English) Zbl 1180.35287 J. Stat. Phys. 135, No. 1, 107-132 (2009). Reviewer: Yaping Liu (Pittsburg) MSC: 35K57 35B40 35K40 PDFBibTeX XMLCite \textit{D. Hilhorst} et al., J. Stat. Phys. 135, No. 1, 107--132 (2009; Zbl 1180.35287) Full Text: DOI
Chipot, Michel; Hilhorst, Danielle; Kinderlehrer, David; Olech, Michał Contraction in \(L^{1}\) for a system arising in chemical reactions and molecular motors. (English) Zbl 1171.35408 Differ. Equ. Appl. 1, No. 1, 139-151 (2009). Reviewer: Cheng He (Beijing) MSC: 35K57 35K50 35A05 PDFBibTeX XMLCite \textit{M. Chipot} et al., Differ. Equ. Appl. 1, No. 1, 139--151 (2009; Zbl 1171.35408) Full Text: DOI Link
Hilhorst, Danielle; Iida, Masato; Mimura, Masayasu; Ninomiya, Hirokazu Relative compactness in \(L^p\) of solutions of some \(2m\) components competition-diffusion systems. (English) Zbl 1149.35361 Discrete Contin. Dyn. Syst. 21, No. 1, 233-244 (2008). MSC: 35K50 35K57 35R35 35B40 PDFBibTeX XMLCite \textit{D. Hilhorst} et al., Discrete Contin. Dyn. Syst. 21, No. 1, 233--244 (2008; Zbl 1149.35361) Full Text: DOI
Chipot, M.; Hilhorst, D.; Kinderlehrer, D.; Olech, M. Contraction in \(L^1\) and large time behavior for a system arising in chemical reactions and molecular motors. arXiv:0808.0250 Preprint, arXiv:0808.0250 [math.AP] (2008). MSC: 34D23 35K45 35K50 35K55 35K57 92C37 92C45 BibTeX Cite \textit{M. Chipot} et al., ``Contraction in $L^1$ and large time behavior for a system arising in chemical reactions and molecular motors'', Preprint, arXiv:0808.0250 [math.AP] (2008) Full Text: arXiv OA License
Crooks, Elaine C. M.; Dancer, E. Norman; Hilhorst, Danielle On long-time dynamics for competition-diffusion systems with inhomogeneous Dirichlet boundary conditions. (English) Zbl 1146.35014 Topol. Methods Nonlinear Anal. 30, No. 1, 1-36 (2007). Reviewer: Rong Yuan (Beijing) MSC: 35B40 35K50 35K57 92D25 35B25 PDFBibTeX XMLCite \textit{E. C. M. Crooks} et al., Topol. Methods Nonlinear Anal. 30, No. 1, 1--36 (2007; Zbl 1146.35014) Full Text: arXiv
Crooks, E. C. M.; Dancer, E. N.; Hilhorst, D. Fast reaction limit and long time behavior for a competition-diffusion system with Dirichlet boundary conditions. (English) Zbl 1139.35049 Discrete Contin. Dyn. Syst., Ser. B 8, No. 1, 39-44 (2007). Reviewer: Eva Sanchez (Madrid) MSC: 35K50 35B40 35K57 92D25 PDFBibTeX XMLCite \textit{E. C. M. Crooks} et al., Discrete Contin. Dyn. Syst., Ser. B 8, No. 1, 39--44 (2007; Zbl 1139.35049) Full Text: DOI
Crooks, E. C. M.; Dancer, E. N.; Hilhorst, D.; Mimura, M.; Ninomiya, H. Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions. (English) Zbl 1079.35008 Nonlinear Anal., Real World Appl. 5, No. 4, 645-665 (2004). Reviewer: Jiaqi Mo (Wuhu) MSC: 35B25 35K50 35K57 92D25 PDFBibTeX XMLCite \textit{E. C. M. Crooks} et al., Nonlinear Anal., Real World Appl. 5, No. 4, 645--665 (2004; Zbl 1079.35008) Full Text: DOI
Hilhorst, D.; Mimura, M.; Weidenfeld, R. Singular limit of a class of non-cooperative reaction-diffusion systems. (English) Zbl 1153.35344 Taiwanese J. Math. 7, No. 3, 391-421 (2003). MSC: 35K40 35B20 35K57 PDFBibTeX XMLCite \textit{D. Hilhorst} et al., Taiwanese J. Math. 7, No. 3, 391--421 (2003; Zbl 1153.35344) Full Text: DOI Link
Bothe, D.; Hilhorst, D. A reaction-diffusion system with fast reversible reaction. (English) Zbl 1039.35013 J. Math. Anal. Appl. 286, No. 1, 125-135 (2003). Reviewer: René Sperb (Zürich) MSC: 35B25 35K57 35K50 PDFBibTeX XMLCite \textit{D. Bothe} and \textit{D. Hilhorst}, J. Math. Anal. Appl. 286, No. 1, 125--135 (2003; Zbl 1039.35013) Full Text: DOI
Hilhorst, Danielle; Mimura, Masayasu; Schätzle, Reiner Vanishing latent heat limit in a Stefan-like problem arising in biology. (English) Zbl 1049.92035 Nonlinear Anal., Real World Appl. 4, No. 2, 261-285 (2003). MSC: 92D40 35K57 35R35 35K65 PDFBibTeX XMLCite \textit{D. Hilhorst} et al., Nonlinear Anal., Real World Appl. 4, No. 2, 261--285 (2003; Zbl 1049.92035) Full Text: DOI
Feireisl, E.; Mimura, M.; Hilhorst, D.; Weidenfeld, R. On some reaction-diffusion systems with nonlinear diffusion arising in biology. (English) Zbl 1074.35047 Berestycki, Henri (ed.) et al., Nonlinear PDEs in condensed matter and reactive flows. Proceedings of the NATO Advanced Study Institute on PDE’s in models of superfluidity, superconductivity and reactive flows, Cargèse, France, 21 June – 3 July 1999. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0972-0/hbk). NATO ASI Ser., Ser. C, Math. Phys. Sci. 569, 115-125 (2002). Reviewer: Wan-Tong Li (Lanzhou) MSC: 35K50 35K57 92D25 PDFBibTeX XMLCite \textit{E. Feireisl} et al., NATO ASI Ser., Ser. C, Math. Phys. Sci. 569, 115--125 (2002; Zbl 1074.35047) Full Text: DOI
Hilhorst, Danielle; Rodrigues, José-Francisco On a nonlocal diffusion equation with discontinuous reaction. (English) Zbl 0990.35058 Adv. Differ. Equ. 5, No. 4-6, 657-680 (2000). Reviewer: Michael A.Borodin (Donetsk) MSC: 35K50 35K57 35R35 35K65 PDFBibTeX XMLCite \textit{D. Hilhorst} and \textit{J.-F. Rodrigues}, Adv. Differ. Equ. 5, No. 4--6, 657--680 (2000; Zbl 0990.35058)
Hilhorst, D.; Peletier, M. A. Convergence to travelling waves in a reaction-diffusion system arising in contaminant transport. (English) Zbl 0963.35020 J. Differ. Equations 163, No. 1, 89-112 (2000). Reviewer: Alberto Tesei (Roma) MSC: 35B40 35K65 35K57 76S05 35K45 PDFBibTeX XMLCite \textit{D. Hilhorst} and \textit{M. A. Peletier}, J. Differ. Equations 163, No. 1, 89--112 (2000; Zbl 0963.35020) Full Text: DOI
Hilhorst, D.; Issard-Roch, F.; Seidman, T. I. On a reaction-diffusion equation with a free boundary: The case of an unbounded domain. (English) Zbl 0798.35166 Chadam, John M. (ed.) et al., Free boundary problems involving solids. Proceedings of the international colloquium ”Free boundary problems: theory and applications”, held in Montreal, Canada, June 13 - June 22, 1990. Harlow, Essex: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 281, 232-236 (1993). MSC: 35R35 35K57 92E99 PDFBibTeX XMLCite \textit{D. Hilhorst} et al., Pitman Res. Notes Math. Ser. 281, 232--236 (1993; Zbl 0798.35166)