Majdoub, Mohamed; Tayachi, Slim Existence and regularity of source-type self-similar solutions for stable thin-film equations. (English) Zbl 1497.35081 Interfaces Free Bound. 24, No. 3, 431-457 (2022). MSC: 35C06 35K35 35K59 35K65 35R35 35B40 35B65 34B16 76A20 PDFBibTeX XMLCite \textit{M. Majdoub} and \textit{S. Tayachi}, Interfaces Free Bound. 24, No. 3, 431--457 (2022; Zbl 1497.35081) Full Text: DOI arXiv
Segatti, Antonio; Vázquez, Juan Luis On a fractional thin film equation. (English) Zbl 1437.35429 Adv. Nonlinear Anal. 9, 1516-1558 (2020). Reviewer: Piotr Biler (Wrocław) MSC: 35K55 35R11 35C06 35D30 35Q35 PDFBibTeX XMLCite \textit{A. Segatti} and \textit{J. L. Vázquez}, Adv. Nonlinear Anal. 9, 1516--1558 (2020; Zbl 1437.35429) Full Text: DOI arXiv
Álvarez-Caudevilla, Pablo; Evans, Jonathan D.; Galaktionov, Victor A. Gradient blow-up for a fourth-order quasilinear Boussinesq-type equation. (English) Zbl 1403.35058 Discrete Contin. Dyn. Syst. 38, No. 8, 3913-3938 (2018). MSC: 35B44 41A60 35C20 35G20 35C06 35L77 PDFBibTeX XMLCite \textit{P. Álvarez-Caudevilla} et al., Discrete Contin. Dyn. Syst. 38, No. 8, 3913--3938 (2018; Zbl 1403.35058) Full Text: DOI
Koçak, Hüseyin Similarity solutions of nonlinear third-order dispersive PDEs: the first critical exponent. (English) Zbl 1377.35019 Appl. Math. Lett. 74, 108-113 (2017). MSC: 35B33 35C06 35B44 PDFBibTeX XMLCite \textit{H. Koçak}, Appl. Math. Lett. 74, 108--113 (2017; Zbl 1377.35019) Full Text: DOI
Liu, Changchun; Tang, Hui Study of weak solutions for a higher order nonlinear degenerate parabolic equation. (English) Zbl 1346.35114 Appl. Anal. 95, No. 9, 1845-1872 (2016). MSC: 35K65 35G25 35K55 PDFBibTeX XMLCite \textit{C. Liu} and \textit{H. Tang}, Appl. Anal. 95, No. 9, 1845--1872 (2016; Zbl 1346.35114) Full Text: DOI
Chugunova, Marina; Taranets, Roman M. Blow-up with mass concentration for the long-wave unstable thin-film equation. (English) Zbl 1338.35226 Appl. Anal. 95, No. 5, 944-962 (2016). MSC: 35K55 35K35 35K65 76A20 76D08 PDFBibTeX XMLCite \textit{M. Chugunova} and \textit{R. M. Taranets}, Appl. Anal. 95, No. 5, 944--962 (2016; Zbl 1338.35226) Full Text: DOI
Liu, Changchun; Zhang, Xiaoli Invariance of the support of solutions for a sixth-order thin film equation. (Invariance du support des solutions d’une équation du sixième ordre modélisant un film mince.) (English. French summary) Zbl 1338.35216 C. R., Math., Acad. Sci. Paris 354, No. 1, 69-73 (2016). MSC: 35K25 35B05 35D30 35K35 PDFBibTeX XMLCite \textit{C. Liu} and \textit{X. Zhang}, C. R., Math., Acad. Sci. Paris 354, No. 1, 69--73 (2016; Zbl 1338.35216) Full Text: DOI
Álvarez-Caudevilla, Pablo; Galaktionov, Victor A. Well-posedness of the Cauchy problem for a fourth-order thin film equation via regularization approaches. (English) Zbl 1320.35174 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 121, 19-35 (2015). MSC: 35K65 35A09 35G20 35K25 PDFBibTeX XMLCite \textit{P. Álvarez-Caudevilla} and \textit{V. A. Galaktionov}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 121, 19--35 (2015; Zbl 1320.35174) Full Text: DOI arXiv
Liu, Changchun; Wang, Zhao Optimal control for a sixth order nonlinear parabolic equation. (English) Zbl 1305.49006 Math. Methods Appl. Sci. 38, No. 2, 247-262 (2015). MSC: 49J20 49K20 35K25 PDFBibTeX XMLCite \textit{C. Liu} and \textit{Z. Wang}, Math. Methods Appl. Sci. 38, No. 2, 247--262 (2015; Zbl 1305.49006) Full Text: DOI
Álvarez-Caudevilla, P.; Evans, J. D.; Galaktionov, V. A. The Cauchy problem for a tenth-order thin film equation. II: Oscillatory source-type and fundamental similarity solutions. (English) Zbl 1515.35138 Discrete Contin. Dyn. Syst. 35, No. 3, 807-827 (2015). MSC: 35K65 35B40 35K30 35K59 37K50 76A20 PDFBibTeX XMLCite \textit{P. Álvarez-Caudevilla} et al., Discrete Contin. Dyn. Syst. 35, No. 3, 807--827 (2015; Zbl 1515.35138) Full Text: DOI arXiv
Li, Yibao; Kim, Junseok Numerical investigations on self-similar solutions of the nonlinear diffusion equation. (English) Zbl 1408.76393 Eur. J. Mech., B, Fluids 42, 30-36 (2013). MSC: 76M20 65M06 35C06 76A20 76R50 PDFBibTeX XMLCite \textit{Y. Li} and \textit{J. Kim}, Eur. J. Mech., B, Fluids 42, 30--36 (2013; Zbl 1408.76393) Full Text: DOI
King, John R.; Taranets, Roman M. Asymmetric travelling waves for the thin film equation. (English) Zbl 1322.35050 J. Math. Anal. Appl. 404, No. 2, 399-419 (2013). Reviewer: Anna Ghazaryan (Oxford, OH) MSC: 35K25 76A20 35R35 35C07 PDFBibTeX XMLCite \textit{J. R. King} and \textit{R. M. Taranets}, J. Math. Anal. Appl. 404, No. 2, 399--419 (2013; Zbl 1322.35050) Full Text: DOI
Agarwal, Ravi P.; Kovacs, B.; O’Regan, D. Positive solutions for a sixth-order boundary value problem with four parameters. (English) Zbl 1297.34029 Bound. Value Probl. 2013, Paper No. 184, 22 p. (2013). MSC: 34B18 34B15 34B09 47N20 PDFBibTeX XMLCite \textit{R. P. Agarwal} et al., Bound. Value Probl. 2013, Paper No. 184, 22 p. (2013; Zbl 1297.34029) Full Text: DOI
Liu, Changchun; Liu, Aibo; Tang, Hui Time-periodic solutions for a driven sixth-order Cahn-Hilliard type equation. (English) Zbl 1293.35017 Bound. Value Probl. 2013, Paper No. 73, 17 p. (2013). MSC: 35B10 35K55 35K65 35K25 35A01 PDFBibTeX XMLCite \textit{C. Liu} et al., Bound. Value Probl. 2013, Paper No. 73, 17 p. (2013; Zbl 1293.35017) Full Text: DOI
Álvarez-Caudevilla, Pablo; Evans, Jonathan D.; Galaktionov, Victor A. The Cauchy problem for a tenth-order thin film equation. I. Bifurcation of oscillatory fundamental solutions. (English) Zbl 1308.35027 Mediterr. J. Math. 10, No. 4, 1761-1792 (2013). Reviewer: Josipa Pina Milisic (Zagreb) MSC: 35B32 35K30 35K65 76A20 35C06 35K59 PDFBibTeX XMLCite \textit{P. Álvarez-Caudevilla} et al., Mediterr. J. Math. 10, No. 4, 1761--1792 (2013; Zbl 1308.35027) Full Text: DOI arXiv
Li, Zhenbang; Liu, Changchun On the nonlinear instability of traveling waves for a sixth-order parabolic equation. (English) Zbl 1257.35061 Abstr. Appl. Anal. 2012, Article ID 739156, 17 p. (2012). MSC: 35C07 35B35 35K30 PDFBibTeX XMLCite \textit{Z. Li} and \textit{C. Liu}, Abstr. Appl. Anal. 2012, Article ID 739156, 17 p. (2012; Zbl 1257.35061) Full Text: DOI
Wang, Zhao; Liu, Changchun Some properties of solutions for the sixth-order Cahn-Hilliard-type equation. (English) Zbl 1258.35113 Abstr. Appl. Anal. 2012, Article ID 414590, 24 p. (2012). MSC: 35K35 35K58 35B44 35B41 PDFBibTeX XMLCite \textit{Z. Wang} and \textit{C. Liu}, Abstr. Appl. Anal. 2012, Article ID 414590, 24 p. (2012; Zbl 1258.35113) Full Text: DOI
Fernandes, R. S.; Galaktionov, V. A. Eigenfunctions and very singular similarity solutions of odd-order nonlinear dispersion PDEs: toward a “nonlinear Airy function” and others. (English) Zbl 1260.35099 Stud. Appl. Math. 129, No. 2, 163-219 (2012). MSC: 35P30 35P20 35A15 PDFBibTeX XMLCite \textit{R. S. Fernandes} and \textit{V. A. Galaktionov}, Stud. Appl. Math. 129, No. 2, 163--219 (2012; Zbl 1260.35099) Full Text: DOI
Álvarez-Caudevilla, P.; Galaktionov, V. A. Local bifurcation-branching analysis of global and “blow-up” patterns for a fourth-order thin film equation. (English) Zbl 1298.35104 NoDEA, Nonlinear Differ. Equ. Appl. 18, No. 5, 483-537 (2011). Reviewer: Svetlana A. Grishina (Ul’yanovsk) MSC: 35K30 35B32 35B44 35C06 35K59 35P05 PDFBibTeX XMLCite \textit{P. Álvarez-Caudevilla} and \textit{V. A. Galaktionov}, NoDEA, Nonlinear Differ. Equ. Appl. 18, No. 5, 483--537 (2011; Zbl 1298.35104) Full Text: DOI arXiv
Liu, Changchun; Tian, Yumei Weak solutions for a sixth-order thin film equation. (English) Zbl 1227.35150 Rocky Mt. J. Math. 41, No. 5, 1547-1565 (2011). MSC: 35K35 35K55 35K65 74K35 76A20 PDFBibTeX XMLCite \textit{C. Liu} and \textit{Y. Tian}, Rocky Mt. J. Math. 41, No. 5, 1547--1565 (2011; Zbl 1227.35150) Full Text: DOI
Galaktionov, V. A. Very singular solutions for thin film equations with absorption. (English) Zbl 1333.35117 Stud. Appl. Math. 124, No. 1, 39-63 (2010). MSC: 35K59 35B40 35K25 35K30 74K35 PDFBibTeX XMLCite \textit{V. A. Galaktionov}, Stud. Appl. Math. 124, No. 1, 39--63 (2010; Zbl 1333.35117) Full Text: DOI arXiv
Galaktionov, V. A. Hermitian spectral theory and blow-up patterns for a fourth-order semilinear Boussinesq equation. (English) Zbl 1191.35230 Stud. Appl. Math. 121, No. 4, 395-431 (2008). Reviewer: Vjacheslav Yurko (Saratov) MSC: 35Q53 35P05 35B40 35B44 PDFBibTeX XMLCite \textit{V. A. Galaktionov}, Stud. Appl. Math. 121, No. 4, 395--431 (2008; Zbl 1191.35230) Full Text: DOI