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Stochastic Analysis and Applications Volume 30, 2012 - Issue 3
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Original Articles

Nonexistence of Global Solutions to Nonlinear Stochastic Wave Equations in Mean Lp-Norm

Pao-Liu Chow Department of Mathematics, Wayne State University, Detroit, Michigan, USACorrespondence[email protected]
Pages 543-551 | Received 15 Aug 2011, Accepted 15 Aug 2011, Published online: 23 Apr 2012

References

  • Bo , L. , Tang , D. , and Wang , Y. 2008 . Explosive solutions of stochastic wave equations with damping in ℝ d . Jour. Diff. Eqs. 244 : 170 – 187 .
  • Chow , P.L. 2002 . Stochastic wave equations with polynomial nonlinearity . Annals of Applied Probability 12 : 1 – 21 .
  • Chow , P.L. 2006 . Asymptotics of solutions to semilinear stochstic wave equations . Annals of Applied Probability 16 : 361 – 381 .
  • Chow , P.L. 2009 . Nonlinear stochastic wave equations: Blow-up of second moments in L 2 norm . Annals of Applied Probability 19 : 2039 – 2046 .
  • Chow , P.L. 2009 . Unbounded positive solutions of nonlinear parabolic It equations . Communications in Stochastic Analysis 2 : 211 – 222 .
  • Chow , P.L. 2007 . Stochastic Partial Differential Equations. Chapman & Hall/CRC, Boca Raton, FL.
  • Evans , L.C. 2010 . Partial Differential Equations . American Mathematical Society , Providence , RI .
  • Glassey , R.T. 1973 . Blow-up theorems for nonlinear wave equations . Math. Z. 132 : 183 – 203 .
  • John , F. 1990 . Nonlinear Wave Equations, Formation of Singularities . American Mathematical Society , Providence , RI .
  • Kaplan , S. 1963 . On the growth of solutions of quasilinear parabolic equations . Communications in Pure Applied Mathematics 16 : 327 – 330 .
  • Keller , J.B. 1957 . On solutions of nonlinear wave equations . Communications in Pure Applied Mathematics 10 : 523 – 530 .
  • Levine , H.A. 1974 . Instability and nonexistence of global solutions to nonlinear wave equations of the form Pu tt  = − Au + ℱ(u) . Transactions of the American Mathematical Society 192 : 1 – 21 .
  • Mueller , C. 1987 . Long time existence for the wave equation with a noise term . Annals of Probability 25 : 133 – 151 .

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