[1] |
Wenying, C.; Yong, Z., Global non existence for a semilinear Petrovsky equation, Nonlinear Anal, 70, 3203-3208 (2009) · Zbl 1157.35324 |
[2] |
Han, X.; Wang, M., Asymptotic behavior for Petrovsky equation with localized damping, Acta Appl Math, 110, 3, 1057-1076 (2010) · Zbl 1191.35058 |
[3] |
Li, G.; Sun, Y.; Liu, W., Global existence, uniform decay and blow-up of solutions for a system of Petrovsky equations, Nonlinear Anal, 74, 4, 1523-1538 (2011) · Zbl 1211.35178 |
[4] |
Li, G.; Sun, Y.; Liu, W., Global existence and blow-up of solutions for a strongly damped Petrovsky system with nonlinear damping, Appl Anal, 91, 3, 575-586 (2012) · Zbl 1242.35062 |
[5] |
Yaojun, Y., Global existence and blow-up of solutions for a system of Petrovsky equations, Appl Anal, 96, 16, 2869-2890 (2017) · Zbl 1375.35280 |
[6] |
Zhou, J., Lower bounds for blow-up time of two nonlinear wave equations, Appl Math Lett, 45, 64-68 (2015) · Zbl 1316.35055 |
[7] |
Wang, Y.; Wang, Y., On the initial-boundary problem for fourth order wave equations with damping, strain and source terms, J Math Anal Appl, 405, 1, 116-127 (2013) · Zbl 1310.35175 |
[8] |
Jun, Z., Global existence and blow-up of solutions for a Kirchhoff type plate equation with damping, Appl Math Comput, 265, 807-818 (2015) · Zbl 1410.35237 |
[9] |
Li, F.; Bai, Y., Uniform rates of decay for nonlinear viscoelastic Marguerrevon Karman shallow shell system, J Math Anal Appl, 351, 522-535 (2009) · Zbl 1155.35058 |
[10] |
Li, F., Limit behavior of the solution to nonlinear viscoelastic Marguerre-von Karman shallow shells system, J Differ Equ, 249, 1241-1257 (2010) · Zbl 1425.74299 |
[11] |
Park, S-H; Kang, J-R., Blow-up of solutions for a viscoelastic wave equation with variable exponents, Math Meth Appl Sci, 42, 2083-2097 (2019) · Zbl 1437.35502 |
[12] |
Park, S-H., Blow-up for a viscoelastic von Karman equation with strong damping and variable exponent source terms, Bound Value Probl, 63, 2021 (2021) · Zbl 1486.35080 · doi:10.1186/s13661-021-01537-2 |
[13] |
Lagnese, JE., Asymptotic energy estimates for Kirchoff plates subject to weak viscoelastic damping (1989), Bassel: Birkhcauser-Verlag, Bassel |
[14] |
Munoz Rivera, JE; Lapa, EC; Barreto, R., Decay rates for viscoelastic plates with memory, J Elast, 44, 61-87 (1996) · Zbl 0876.73037 |
[15] |
Alabau-Boussouira, F.; Cannarsa, P.; Sforza, D., Decay estimates for the second order evaluation equation with memory, J Funct Anal, 254, 1342-1372 (2008) · Zbl 1145.35025 |
[16] |
Liu, L.; Sun, F.; Wu, Y., Blow-up of solutions for a nonlinear Petrovsky type equation with initial data at arbitrary high energy level, Bound Value Probl, 15, 2019 (2019) · Zbl 1513.35390 · doi:10.1186/s13661-019-1136-x |
[17] |
Fushan, L.; Qingyong, G., Blow-up of solution for a nonlinear Petrovsky type equation with memory, Appl Math Comput, 274, 383-392 (2016) · Zbl 1410.35085 |
[18] |
Tahamtani, F.; Shahrouzi, M., Existence and blow up of solutions to a Petrovsky equation withmemory and nonlinear source term, Bound Value Probl, 2012, 50 (2012) · Zbl 1275.35151 |
[19] |
Li, G.; Sun, Y.; Liu, W., On a symptotic behavior and blow-up of solutions for a nonlinear viscoelastic Petrovsky equation with positive initial energy, J Funct Spaces Appl, 2013 (2013) · Zbl 1270.35299 |
[20] |
Aboulaich, R.; Meskine, D.; Souissi, A., New diffusion models in image processing, Comput Math Appl, 56, 874-882 (2008) · Zbl 1155.35389 |
[21] |
Kbiri Alaoui, M.; Nabil, T.; Altanji, M., On some new nonlinear diffusion model for the image filtering, Appl Anal, 93, 2, 269-280 (2013) · Zbl 1295.35270 |
[22] |
Songzhe, L.; Gao, W.; Cao, C., Study of the solutions to a model porousmedium equation with variable exponent of nonlinearity, J Math Anal Appl, 342, 27-38 (2008) · Zbl 1140.35497 |
[23] |
Ting, TW., Certain non-steady flows of second-order fluids, Arch Ration Mech Anal, 14, 1-26 (1963) · Zbl 0139.20105 |
[24] |
Korpusov, MO; Sveshnikov, AG., Blow-up of solutions of Sobolev-type nonlinear equations with cubic sources, J Differ Equ, 42, 431-443 (2006) · Zbl 1131.35073 |
[25] |
Diening, L.; Růžička, M., Calderó n-Zygmund operators on generalized Lebesgue spaces \(####\) and problems related to fluid dynamics, J Reine Angew Math, 563, 197-220 (2003) · Zbl 1072.76071 |
[26] |
Samarskii, AA; Galaktionov, VA; Kurdyumov, SP, Blow-up in quasilinear parabolic equations (1995), Berlin (NY): Walter de Gruyter, Berlin (NY) · Zbl 1020.35001 |
[27] |
Pinasco, JP., Blow-up for parabolic and hyperbolic problems with variable exponents, Nonlinear Anal Theory Methods Appl, 71, 1094-1099 (2009) · Zbl 1170.35341 |
[28] |
Halsey, TC., Electrorheological fluids, Science, 258, 761-766 (1992) |
[29] |
Acerbi, E.; Mingione, G., Regularity results for electrorheological fluids, the stationary case, C R Acad Sci Paris, 334, 817-822 (2002) · Zbl 1017.76098 |
[30] |
Růžička, M., Lecture Notes in Mathematics, 1748, Electrorheological fluids, modeling and mathematical theory (2000), New York: Springer, New York · Zbl 0968.76531 |
[31] |
Diening, L.; Hästo, P.; Harjulehto, P., Lebesgue and Sobolev spaces with variable exponents (2011), Berlin: Springer-Verlag, Berlin · Zbl 1222.46002 |
[32] |
Michael, R.; Barry, S., Scattering theory, III (1979), London, New York: Academic Press, London, New York · Zbl 0405.47007 |
[33] |
Erich, Z., Partial differential equations of applied mathematics, Pure and Applied Mathematics, seconded (1989), New York (NY): A Wiley-Interscience Publication, John Wiley and Sons, Inc, New York (NY) · Zbl 0699.35003 |
[34] |
Abita, R., Existence and asymptotic stability for the semilinear wave equation with variable-exponent nonlinearities, J Math Phys, 60 (2019) · Zbl 1435.35256 |
[35] |
Lions, JL., Quelques méthodes de résolution des problèmes aux limites non linéaires (1966), Paris: Dunod, Paris |
[36] |
Lions, JL; Magenes, E., Problemes aux limites nonhomog ènes et applications (1968), Paris: Dunod, Paris · Zbl 0165.10801 |
[37] |
Abita, R., Existence and asymptotic behavior of solutions for degenerate nonlinear Kirchhoff strings with variable-exponent nonlinearities, Acta Math Vietnam, 46, 613-643 (2021) · Zbl 1471.35204 |
[38] |
Kalantarov, V.; Ladyzhenskaya, OA., The occurence of collapse for quasilinear equation of paprabolic and hyperbolic types, J Sov Math, 10, 53-70 (1978) · Zbl 0388.35039 |
[39] |
Payne, LE., Improperly posed problems in partial differential equations, Regional Conference Series in Applied Mathematics (1975), Pennsylvania (PA): Society for industrial and applied mathematics, Pennsylvania (PA) · Zbl 0302.35003 |
[40] |
Levin, HA., Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu####\), Arch Ration Mech Anal, 51, 371-386 (1973) · Zbl 0278.35052 |
[41] |
Ali, K.; Khadijeh, B., Blow-up in a semilinear parabolic problem with variable source under positive initial energy, Appl Anal, 94, 9, 1888-1896 (2015) · Zbl 1331.35194 |
[42] |
Abita, R., Blow-up phenomenon for a semilinear pseudo-parabolic equation involving variable source, Appl Anal, 1-16 (2021) |
[43] |
Abita, R., Blow-up phenomenon for a semilinear pseudo-parabolic equation involving variable source, Appl Anal, 101, 6, 1871-1879 (2020) |