On wave equations of the p-Laplacian type with supercritical nonlinearities

Adams, 1975, vol. 65 Agre, 2006, Systems of nonlinear wave equations with damping and source terms, Differ. Integral Equ., 19, 1235 Alves, 2009, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms, Discret. Contin. Dyn. Syst. Ser. S, 2, 583 Barbu, 2010 Barbu, 2005, On nonlinear wave equations with degenerate damping and source terms, Trans. Amer. Math. Soc., 357, 2571, 10.1090/S0002-9947-05-03880-8 Barbu, 2005, Existence and uniqueness of solutions to wave equations with nonlinear degenerate damping and source terms, Control Cybern., 34, 665 Barbu, 2007, Blow-up of generalized solutions to wave equations with nonlinear degenerate damping and source terms, Indiana Univ. Math. J., 56, 995, 10.1512/iumj.2007.56.2990 Benaissa, 2007, Decay estimates for the wave equation of p-Laplacian type with dissipation of m-Laplacian type, Math. Methods Appl. Sci., 30, 237, 10.1002/mma.789 Biazutti, 1995, On a nonlinear evolution equation and its applications, Nonlinear Anal., 24, 1221, 10.1016/0362-546X(94)00193-L Bociu, 2008, Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping, Appl. Math. (Warsaw), 35, 281, 10.4064/am35-3-3 Bociu, 2008, Uniqueness of weak solutions for the semilinear wave equations with supercritical boundary/interior sources and damping, Discrete Contin. Dyn. Syst., 22, 835, 10.3934/dcds.2008.22.835 Bociu, 2010, Local Hadamard well-posedness for nonlinear wave equations with supercritical sources and damping, J. Differential Equations, 249, 654, 10.1016/j.jde.2010.03.009 Boyer, 2013 Chen, 1998, Long time behavior of strongly damped nonlinear wave equations, J. Differential Equations, 147, 231, 10.1006/jdeq.1998.3447 Chueshov, 2002, On the attractor for a semilinear wave equation with critical exponent and nonlinear boundary dissipation, Comm. Partial Differential Equations, 27, 1901, 10.1081/PDE-120016132 Cuesta, 2001, Eigenvalue problems for the p-Laplacian with indefinite weights, Electron. J. Differ. Equ., 9, 33 Georgiev, 1994, Existence of a solution of the wave equation with nonlinear damping and source terms, J. Differential Equations, 109, 295, 10.1006/jdeq.1994.1051 Ghidaglia, 1991, Longtime behaviour of strongly damped wave equations global attractors and their dimension, SIAM J. Math. Anal., 22, 879, 10.1137/0522057 Glassey, 1973, Blow-up theorems for nonlinear wave equations, Math. Z., 132, 183, 10.1007/BF01213863 Guo, 2013, Blow-up of solutions to systems of nonlinear wave equations with supercritical sources, Appl. Anal., 92, 1101, 10.1080/00036811.2011.649734 Guo, 2013, Global existence and decay of energy to systems of wave equations with damping and supercritical sources, Z. Angew. Math. Phys., 64, 621, 10.1007/s00033-012-0252-6 Guo, 2014, Systems of nonlinear wave equations with damping and supercritical boundary and interior sources, Trans. Amer. Math. Soc., 366, 2265, 10.1090/S0002-9947-2014-05772-3 Huang, 1990, On eigenvalue problems of p-Laplacian with Neumann boundary conditions, Proc. Amer. Math. Soc., 109, 177 Kass, 2018, Local and global existence of solutions to a strongly damped wave equation of the p-Laplacian type, Commun. Pure Appl. Anal., 17, 1449, 10.3934/cpaa.2018070 Lê, 2006, Eigenvalue problems for the p-Laplacian, Nonlinear Anal., 64, 1057, 10.1016/j.na.2005.05.056 Levine, 1974, Instability and nonexistence of global solutions to nonlinear wave equations of the form Putt=−Au+F(u), Trans. Amer. Math. Soc., 192, 1 Levine, 1997, Global nonexistence theorems for quasilinear evolution equations with dissipation, Arch. Ration. Mech. Anal., 137, 341, 10.1007/s002050050032 Lions, 1972 Lions, 1965, Some non-linear evolution equations, Bull. Soc. Math. France, 93, 43, 10.24033/bsmf.1616 Nakao, 1975, Existence of global (bounded) solutions for some nonlinear evolution equations of second order, Math. Rep. College General Ed. Kyushu Univ., 10, 67 Payne, 1975, Saddle points and instability of nonlinear hyperbolic equations, Israel J. Math., 22, 273, 10.1007/BF02761595 Pei, 2015, Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources, J. Math. Phys., 56, 10.1063/1.4927688 Radu, 2005, Weak solutions to the Cauchy problem of a semilinear wave equation with damping and source terms, Adv. Differ. Equ., 10, 1261 Radu, 2008, Weak solutions to the initial boundary value problem for a semilinear wave equation with damping and source terms, Appl. Math. (Warsaw), 35, 355, 10.4064/am35-3-7 Rammaha, 2012, Hadamard well-posedness for wave equations with p-Laplacian damping and supercritical sources, Adv. Differential Equations, 17, 105 Showalter, 1997, Vol. 49 Torné, 2005, Steklov problem with an indefinite weight for the p-Laplacian, Electron. J Differ. Equ., 8, 87 Tsouli, 2017, Nonlinear eigenvalue problem for the p-laplacian, Commun. Math. Anal., 20, 69 Vitillaro, 2000, Some new results on global nonexistence and blow-up for evolution problems with positive initial energy, Rend. Istit. Mat. Univ. Trieste, 31, 245 Vitillaro, 2002, Global existence for the wave equation with nonlinear boundary damping and source terms, J. Differential Equations, 186, 259, 10.1016/S0022-0396(02)00023-2 Vitillaro, 2002, A potential well theory for the wave equation with nonlinear source and boundary damping terms, Glasg. Math. J., 44, 375, 10.1017/S0017089502030045 Webb, 1980, Existence and asymptotic behavior for a strongly damped nonlinear wave equation, Canad. J. Math., 32, 631, 10.4153/CJM-1980-049-5