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Explosive solutions of stochastic viscoelastic wave equations with multiplicative noises. (English) Zbl 1333.60139
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
35B44 Blow-up in context of PDEs
35L05 Wave equation
35L70 Second-order nonlinear hyperbolic equations
Full Text: DOI
[1] 1. M. Kafini and S. A. Messaoudi, A blow-up result in a Cauchy viscoelastic problem, Appl. Math. Lett.21 (2008) 549-553. genRefLink(16, ’S0129055X15500221BIB001’, ’10.1016%252Fj.aml.2007.07.004’); genRefLink(128, ’S0129055X15500221BIB001’, ’000255792100003’); · Zbl 1149.35076
[2] 2. S. A. Messaoudi, Blow up and global existence in a nonlinear viscoelastic wave equation, Math. Nachr.260 (2003) 58-66. genRefLink(16, ’S0129055X15500221BIB002’, ’10.1002%252Fmana.200310104’); genRefLink(128, ’S0129055X15500221BIB002’, ’000186704900006’);
[3] 3. S. A. Messaoudi, Blow up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation, J. Math. Anal. Appl.320 (2006) 902-915. genRefLink(16, ’S0129055X15500221BIB003’, ’10.1016%252Fj.jmaa.2005.07.022’); genRefLink(128, ’S0129055X15500221BIB003’, ’000238002400033’); · Zbl 1098.35031
[4] 4. H. T. Song and C. K. Zhong, Blow-up of solutions of a nonlinear viscoelastic wave equation, Nonlinear Anal.11 (2010) 3877-3883. genRefLink(16, ’S0129055X15500221BIB004’, ’10.1016%252Fj.nonrwa.2010.02.015’); genRefLink(128, ’S0129055X15500221BIB004’, ’000281390000052’); · Zbl 1213.35143
[5] 5. Y. J. Wang, A global nonexistence theorem for viscoelastic equations with arbitrarily positive initial energy, Appl. Math. Lett.22 (2009) 1394-1400. genRefLink(16, ’S0129055X15500221BIB005’, ’10.1016%252Fj.aml.2009.01.052’); genRefLink(128, ’S0129055X15500221BIB005’, ’000267964200017’); · Zbl 1173.35575
[6] 6. L. Payne and D. Sattinger, Saddle points and instability on nonlinear hyperbolic equations, Israel Math. J.22 (1975) 273-303. genRefLink(16, ’S0129055X15500221BIB006’, ’10.1007%252FBF02761595’); genRefLink(128, ’S0129055X15500221BIB006’, ’A1975BE24100009’);
[7] 7. H. A. Levine and J. Serrin, Global nonexistence theorems for quasilinear evolution equation with dissipation, Arch. Ration. Mech. Anal.137 (1997) 341-361. genRefLink(16, ’S0129055X15500221BIB007’, ’10.1007%252Fs002050050032’); genRefLink(128, ’S0129055X15500221BIB007’, ’A1997XK86200003’);
[8] 8. H. A. Levine and S. R. Park, Global existence and global nonexistence of solutions of the Cauchy problem for a nonlinearly damped wave equation, J. Math. Anal. Appl.228 (1998) 181-205. genRefLink(16, ’S0129055X15500221BIB008’, ’10.1006%252Fjmaa.1998.6126’); genRefLink(128, ’S0129055X15500221BIB008’, ’000077363300014’);
[9] 9. E. Vitillaro, Global nonexistence theorems for a class of evolution equations with dissipation, Arch. Ration. Mech. Anal.149 (1999) 155-182. genRefLink(16, ’S0129055X15500221BIB009’, ’10.1007%252Fs002050050171’); genRefLink(128, ’S0129055X15500221BIB009’, ’000083836200003’);
[10] 10. Z. J. Yang, Existence and asymptotic behavior of solutions for a class of quasi-linear evolution equations with non-linear damping and source terms, Math. Methods Appl. Sci.25 (2002) 795-814. genRefLink(16, ’S0129055X15500221BIB010’, ’10.1002%252Fmma.306’); genRefLink(128, ’S0129055X15500221BIB010’, ’000176565100001’);
[11] 11. S. A. Messaoudi and B. Said-Houari, Blow up of solutions of a class of wave equations with nonlinear damping and source terms, Math. Methods Appl. Sci.27 (2004) 1687-1696. genRefLink(16, ’S0129055X15500221BIB011’, ’10.1002%252Fmma.522’); genRefLink(128, ’S0129055X15500221BIB011’, ’000224148500006’); · Zbl 1073.35178
[12] 12. T. T. Wei and Y. M. Jiang, Stochastic wave equations with memory, Chin. Ann. Math. B31 (2010) 329-342. genRefLink(16, ’S0129055X15500221BIB012’, ’10.1007%252Fs11401-009-0170-x’); genRefLink(128, ’S0129055X15500221BIB012’, ’000278152200004’);
[13] 13. F. Liang and H. J. Gao, Explosive solutions of stochastic viscoelastic wave equations with damping, Rev. Math. Phys.23 (2011) 883-902. [Abstract] genRefLink(128, ’S0129055X15500221BIB013’, ’000295274500004’); genRefLink(64, ’S0129055X15500221BIB013’, ’2011RvMaP..23..883L’); · Zbl 1229.60080
[14] 14. F. Liang and H. J. Gao, Global existence and explosive solution for stochastic viscoelastic wave equation with nonlinear damping, Rev. Math. Phys.26(7) (2014) 1450013, 35pp. [Abstract] genRefLink(128, ’S0129055X15500221BIB014’, ’000341933500003’);
[15] 15. S. T. Wu and L. Y. Tsai, Blow-up of solutions for some non-linear wave equations of Kirchhoff type with some dissipation, Nonlinear Anal.65 (2006) 243-264. genRefLink(16, ’S0129055X15500221BIB015’, ’10.1016%252Fj.na.2004.11.023’); genRefLink(128, ’S0129055X15500221BIB015’, ’000238581700001’); · Zbl 1151.35052
[16] 16. P. L. Chow, Stochastic wave equations with polynomial nonlinearity, Ann. Appl. Probab.12 (2002) 361-381. genRefLink(16, ’S0129055X15500221BIB016’, ’10.1214%252Faoap%252F1015961168’); genRefLink(128, ’S0129055X15500221BIB016’, ’000174617000015’);
[17] 17. Z. Brzeźniak, B. Maslowski and J. Seidler, Stochastic nonlinear beam equations, Probab. Theory Related Fields132 (2005) 119-149. genRefLink(16, ’S0129055X15500221BIB017’, ’10.1007%252Fs00440-004-0392-5’); genRefLink(128, ’S0129055X15500221BIB017’, ’000228285100006’);
[18] 18. M. R. Li and L. Y. Tsai, Existence and nonexistence of global solutions of some systems of semilinear wave equations, Nonlinear Anal.54 (2003) 1397-1415. genRefLink(16, ’S0129055X15500221BIB018’, ’10.1016%252FS0362-546X%252803%252900192-5’); genRefLink(128, ’S0129055X15500221BIB018’, ’000184723300003’);
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