\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Classical solutions to quasilinear parabolic problems with dynamic boundary conditions

Abstract Related Papers Cited by
  • We study linear nonautonomous parabolic systems with dynamic boundary conditions. Next, we apply these results to show a theorem of local existence and uniqueness of a classical solution to a second order quasilinear system with nonlinear dynamic boundary conditions.
    Mathematics Subject Classification: Primary: 35K55; Secondary: 35K15.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    G. Coclite, G. Ruiz Goldstein and J. A. Goldstein, Stability of parabolic problems with nonlinear Wentzell boundary conditions, J. Differential Equations, 246 (2009), 2434-2447.doi: 10.1016/j.jde.2008.10.004.

    [2]

    G. Coclite, G. Ruiz Goldstein and J. A. Goldstein, Well-posedness of nonlinear parabolic problems with nonlinear Wentzell boundary conditions, Adv. Differential Equations, 16 (2011), 895-916.

    [3]

    J. Escher, Quasilinear parabolic systems with dynamical boundary conditions, Comm. Partial Differential Equations, 18 (1993), 1309-1364.doi: 10.1080/03605309308820976.

    [4]

    A. Favini, G. Ruiz Goldstein, J. Goldstein and S. Romanelli, Nonlinear boundary conditions for nonlinear second order differential operators on $C[0, 1]$, Arch. Math. (Basel), 76 (2001), 391-400.doi: 10.1007/PL00000449.

    [5]

    C. Gal and M. Warma, Well posedness and the global attractor of some quasi-linear parabolic equations with nonlinear dynamic boundary conditions, Differential Integral Equations, 23 (2010), 327-358.

    [6]

    D. Guidetti, Linear parabolic problems with dynamic boundary conditions in spaces of H\"older continuous functions, Ann. Mat. Pura Appl. (4), 195 (2016), 167-198.doi: 10.1007/s10231-014-0457-8.

    [7]

    T. Hintermann, Evolution equations with dynamic boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A, 113 (1989), 43-60.doi: 10.1017/S0308210500023945.

    [8]

    J. Kakŭr, Nonlinear parabolic equations with the mixed nonlinear and nonstationary boundary conditions, Math. Slovaca, 30 (1980), 213-237.

    [9]

    M. Warma, The Robin and Wentzell-Robin Laplacians on Lipschitz domains, Semigroup Forum, 73 (2006), 10-30.doi: 10.1007/s00233-006-0617-2.

    [10]

    M. Warma, Quasilinear parabolic equations with nonlinear Wentzell-Robin type boundary conditions, J. Math. Anal. Appl., 336 (2007), 1132-1148.doi: 10.1016/j.jmaa.2007.03.050.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(156) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return