Keita, Sana; Beljadid, Abdelaziz; Bourgault, Yves Mass-conservative and positivity preserving second-order semi-implicit methods for high-order parabolic equations. (English) Zbl 07512373 J. Comput. Phys. 440, Article ID 110427, 25 p. (2021). MSC: 35Kxx 65Mxx 35Qxx PDFBibTeX XMLCite \textit{S. Keita} et al., J. Comput. Phys. 440, Article ID 110427, 25 p. (2021; Zbl 07512373) Full Text: DOI arXiv
Degtyarev, Sergey Classical solvability of the multidimensional free boundary problem for the thin film equation with quadratic mobility in the case of partial wetting. (English) Zbl 1360.35326 Discrete Contin. Dyn. Syst. 37, No. 7, 3625-3699 (2017). MSC: 35R35 35K55 35K65 PDFBibTeX XMLCite \textit{S. Degtyarev}, Discrete Contin. Dyn. Syst. 37, No. 7, 3625--3699 (2017; Zbl 1360.35326) Full Text: DOI arXiv
Liang, Bo; Peng, Xiting; Shen, Huiying Study of solutions to a fourth order parabolic equation. (English) Zbl 1488.35288 Math. Model. Anal. 21, No. 1, 1-15 (2016). MSC: 35K35 35K59 35A01 35A02 35B40 PDFBibTeX XMLCite \textit{B. Liang} et al., Math. Model. Anal. 21, No. 1, 1--15 (2016; Zbl 1488.35288) Full Text: DOI
Shao, Yuanzhen Continuous maximal regularity on singular manifolds and its applications. (English) Zbl 1348.53048 Evol. Equ. Control Theory 5, No. 2, 303-335 (2016). MSC: 53C21 53C44 58J99 35K55 35K65 35K67 35R01 74K15 PDFBibTeX XMLCite \textit{Y. Shao}, Evol. Equ. Control Theory 5, No. 2, 303--335 (2016; Zbl 1348.53048) Full Text: DOI arXiv
Degtyarev, S. P. Liouville property for solutions of the linearized degenerate thin film equation of fourth order in a halfspace. (English) Zbl 1347.35053 Result. Math. 70, No. 1-2, 137-161 (2016). MSC: 35B53 35K35 35K65 35Q35 35A02 76A20 PDFBibTeX XMLCite \textit{S. P. Degtyarev}, Result. Math. 70, No. 1--2, 137--161 (2016; Zbl 1347.35053) Full Text: DOI arXiv
Peng, Xiting; Liang, Bo; Pang, Min; Wang, Ying A viscous thin-film equation with a singular diffusion. (English) Zbl 1515.35143 Bound. Value Probl. 2016, Paper No. 142, 13 p. (2016). MSC: 35K67 35K35 35K58 35K65 76A20 PDFBibTeX XMLCite \textit{X. Peng} et al., Bound. Value Probl. 2016, Paper No. 142, 13 p. (2016; Zbl 1515.35143) Full Text: DOI
Álvarez-Caudevilla, P.; Evans, J. D.; Galaktionov, V. A. Towards optimal regularity for the fourth-order thin film equation in \(\mathbb R^N\): Graveleau-type focusing self-similarity. (English) Zbl 1322.35051 J. Math. Anal. Appl. 431, No. 2, 1099-1123 (2015). MSC: 35K30 35B65 PDFBibTeX XMLCite \textit{P. Álvarez-Caudevilla} et al., J. Math. Anal. Appl. 431, No. 2, 1099--1123 (2015; Zbl 1322.35051) Full Text: DOI arXiv
Liang, Bo; Wang, Meishan; Cao, Yang; Shen, Huiying A thin film equation with a singular diffusion. (English) Zbl 1364.76019 Appl. Math. Comput. 227, 1-10 (2014). MSC: 76A20 76M10 65M60 35K25 PDFBibTeX XMLCite \textit{B. Liang} et al., Appl. Math. Comput. 227, 1--10 (2014; Zbl 1364.76019) Full Text: DOI
Carlen, Eric; Ulusoy, Süleyman Localization, smoothness, and convergence to equilibrium for a thin film equation. (English) Zbl 1515.35048 Discrete Contin. Dyn. Syst. 34, No. 11, 4537-4553 (2014). MSC: 35B40 35A15 35K30 35K59 35K65 76A20 PDFBibTeX XMLCite \textit{E. Carlen} and \textit{S. Ulusoy}, Discrete Contin. Dyn. Syst. 34, No. 11, 4537--4553 (2014; Zbl 1515.35048) Full Text: DOI arXiv
Min, Lihua; Yang, Xiaoping Finite speed of propagation and algebraic time decay of solutions to a generalized thin film equation. (English) Zbl 1277.35221 Commun. Pure Appl. Anal. 13, No. 2, 543-566 (2014). MSC: 35K65 35K35 76A20 35K55 35B40 PDFBibTeX XMLCite \textit{L. Min} and \textit{X. Yang}, Commun. Pure Appl. Anal. 13, No. 2, 543--566 (2014; Zbl 1277.35221) Full Text: DOI
Arliyabi, Ali; Boutat, Mohammed; Hilout, Saïd On the Rayleigh-Plateau instability. (English) Zbl 1265.35132 Appl. Math., Ser. B (Engl. Ed.) 27, No. 2, 127-138 (2012). MSC: 35K55 35R25 47J35 PDFBibTeX XMLCite \textit{A. Arliyabi} et al., Appl. Math., Ser. B (Engl. Ed.) 27, No. 2, 127--138 (2012; Zbl 1265.35132) Full Text: DOI
Liu, Xiaochuan; Qu, Changzheng Existence and blow-up of weak solutions for a sixth-order equation related to thin solid films. (English) Zbl 1203.35127 Nonlinear Anal., Real World Appl. 11, No. 5, 4214-4222 (2010). MSC: 35K35 35K58 76A20 35B44 PDFBibTeX XMLCite \textit{X. Liu} and \textit{C. Qu}, Nonlinear Anal., Real World Appl. 11, No. 5, 4214--4222 (2010; Zbl 1203.35127) Full Text: DOI
Rakotoson, J. Emile; Rakotoson, J. Michel; Verbeke, Cédric Higher order equations related to thin films: Blow-up and global existence, the influence of the initial data. (English) Zbl 1144.35025 J. Differ. Equations 244, No. 11, 2693-2740 (2008). MSC: 35K35 35K55 76A20 PDFBibTeX XMLCite \textit{J. E. Rakotoson} et al., J. Differ. Equations 244, No. 11, 2693--2740 (2008; Zbl 1144.35025) Full Text: DOI
Boutat, M.; Hilout, S.; Rakotoson, J.-E.; Rakotoson, J.-M. The generalized thin film equation with periodic-domain conditions. (English) Zbl 1134.35068 Appl. Math. Lett. 21, No. 1, 101-104 (2008). MSC: 35K65 35K35 35K55 76A20 PDFBibTeX XMLCite \textit{M. Boutat} et al., Appl. Math. Lett. 21, No. 1, 101--104 (2008; Zbl 1134.35068) Full Text: DOI
Boutat, Mohammed; Hilout, Saïd; D’Angelo, Yves; Lods, Véronique An interface evolution problem in the axisymmetric case. (Sur un problème d’évolution d’interface dans le cas axisymétrique.) (French. Abridged English version) Zbl 1142.76331 C. R., Math., Acad. Sci. Paris 341, No. 3, 195-200 (2005). MSC: 76A20 35Q72 76D03 76E17 PDFBibTeX XMLCite \textit{M. Boutat} et al., C. R., Math., Acad. Sci. Paris 341, No. 3, 195--200 (2005; Zbl 1142.76331) Full Text: DOI
Boutat, Mohammed; D’Angelo, Yves; Hilout, Saïd; Lods, Véronique Finite-time blow-up for a thin-film surface evolution problem. (Explosion en temps fini de la solution d’un problème d’évolution de surface de film mince.) (French) Zbl 1055.35127 C. R., Math., Acad. Sci. Paris 337, No. 8, 549-552 (2003). MSC: 35Q72 74N20 80A30 PDFBibTeX XMLCite \textit{M. Boutat} et al., C. R., Math., Acad. Sci. Paris 337, No. 8, 549--552 (2003; Zbl 1055.35127) Full Text: DOI