Ishige, Kazuhiro; Kawakami, Tatsuki; Okabe, Shinya Existence of solutions to nonlinear parabolic equations via majorant integral kernel. (English) Zbl 1495.35096 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 223, Article ID 113025, 22 p. (2022). MSC: 35K30 35K08 35K58 35R11 45G10 PDFBibTeX XMLCite \textit{K. Ishige} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 223, Article ID 113025, 22 p. (2022; Zbl 1495.35096) Full Text: DOI arXiv
Qin, Dandan; Tan, Jiawei; Liu, Bo; Huang, Wenzhu A B-spline finite element method for solving a class of nonlinear parabolic equations modeling epitaxial thin-film growth with variable coefficient. (English) Zbl 1482.65187 Adv. Difference Equ. 2020, Paper No. 172, 26 p. (2020); correction ibid. 2020, Paper No. 371, 1 p. (2020). MSC: 65M60 65M12 35K55 35K35 74K35 PDFBibTeX XMLCite \textit{D. Qin} et al., Adv. Difference Equ. 2020, Paper No. 172, 26 p. (2020; Zbl 1482.65187) Full Text: DOI
Bowen, M.; Witelski, T. P. Pressure-dipole solutions of the thin-film equation. (English) Zbl 1427.35198 Eur. J. Appl. Math. 30, No. 2, 358-399 (2019). MSC: 35Q35 76A20 35K65 35K25 35K59 PDFBibTeX XMLCite \textit{M. Bowen} and \textit{T. P. Witelski}, Eur. J. Appl. Math. 30, No. 2, 358--399 (2019; Zbl 1427.35198) 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
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
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
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
Taranets, Roman M.; King, John R. On an unstable thin-film equation in multi-dimensional domains. (English) Zbl 1302.35222 NoDEA, Nonlinear Differ. Equ. Appl. 21, No. 1, 105-128 (2014). MSC: 35K65 35K35 35Q35 35B45 35K59 76A20 PDFBibTeX XMLCite \textit{R. M. Taranets} and \textit{J. R. King}, NoDEA, Nonlinear Differ. Equ. Appl. 21, No. 1, 105--128 (2014; Zbl 1302.35222) Full Text: DOI
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
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
Zhao, Xiaopeng; Zhang, Min; Liu, Changchun Some properties of solutions for a fourth-order parabolic equation. (English) Zbl 1259.35043 Math. Methods Appl. Sci. 36, No. 2, 169-181 (2013). MSC: 35B41 35K35 76A20 35K59 PDFBibTeX XMLCite \textit{X. Zhao} et al., Math. Methods Appl. Sci. 36, No. 2, 169--181 (2013; Zbl 1259.35043) Full Text: DOI
Lisini, Stefano; Matthes, Daniel; Savaré, Giuseppe Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. (English) Zbl 1248.35095 J. Differ. Equations 253, No. 2, 814-850 (2012). MSC: 35K35 35K59 35B09 35D30 PDFBibTeX XMLCite \textit{S. Lisini} et al., J. Differ. Equations 253, No. 2, 814--850 (2012; Zbl 1248.35095) Full Text: DOI arXiv
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
Galaktionov, V. A. Incomplete self-similar blow-up in a semilinear fourth-order reaction-diffusion equation. (English) Zbl 1196.35058 Stud. Appl. Math. 124, No. 4, 347-381 (2010). MSC: 35B44 35K57 35K58 35K30 35C06 PDFBibTeX XMLCite \textit{V. A. Galaktionov}, Stud. Appl. Math. 124, No. 4, 347--381 (2010; Zbl 1196.35058) Full Text: DOI arXiv
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
Hsu, Shu-Yu Removable singularity of the polyharmonic equation. (English) Zbl 1184.35008 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 2, 624-627 (2010). MSC: 35A20 35B65 35J30 PDFBibTeX XMLCite \textit{S.-Y. Hsu}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 2, 624--627 (2010; Zbl 1184.35008) Full Text: DOI arXiv
Galaktionov, V. A. Three types of self-similar blow-up for the fourth-order \(p\)-Laplacian equation with source. (English) Zbl 1207.35196 J. Comput. Appl. Math. 223, No. 1, 326-355 (2009). MSC: 35K65 35K55 35K35 35B05 PDFBibTeX XMLCite \textit{V. A. Galaktionov}, J. Comput. Appl. Math. 223, No. 1, 326--355 (2009; Zbl 1207.35196) Full Text: DOI
Galaktionov, V. A. On blow-up space jets for the Navier-Stokes equations in \(\mathbb R^{3}\) with convergence to Euler equations. (English) Zbl 1159.81322 J. Math. Phys. 49, No. 11, 113101, 28 p. (2008). MSC: 35Q30 35B44 76D05 PDFBibTeX XMLCite \textit{V. A. Galaktionov}, J. Math. Phys. 49, No. 11, 113101, 28 p. (2008; Zbl 1159.81322) Full Text: DOI