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Applicable Analysis
An International Journal
Volume 87, 2008 - Issue 7
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Original Articles

The lifespan for general quasilinear wave equation with localized dissipation in exterior domains

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Pages 787-803 | Received 01 Apr 2008, Accepted 13 Jun 2008, Published online: 29 Sep 2008

References

  • John , F . 1981 . Blow-up for quasilinear wave equations in three space dimensions . Comm. Pure Appl. Math. , 34 : 29 – 51 .
  • Sideris , TC . 1983 . Global behaviour of solutions to non-linear wave equations in three dimensions . Comm. Partial Diff. Eqns. , 8 : 1291 – 1323 .
  • Keel , M , Smith , H and Sogge , CD . 2004 . Almost global existence for quasilinear wave equations in three space dimensions . J. Amer. Math. Soc. , 17 : 109 – 153 .
  • Metcalfe , J and Sogge , CD . 2005 . Hyperbolic trapped rays and global existence of quasilinear wave equations . Invent. Math. , 159 : 75 – 117 .
  • Morawetz , CS , Ralston , J and Strauss , W . 1977 . Decay of solutions of the wave equation outside nontrapping obstacles . Comm. Pure Appl. Math. , 30 : 447 – 508 .
  • Ikawa , M . 1982 . Decay of solutions of the wave equation in the exterior of two convex bodies . Osaka J. Math. , 19 : 459 – 509 .
  • Ikawa , M . 1998 . Decay of solutions of the wave equation in the exterior of several convex bodies . Ann. Inst. Fourier (Grenoble) , 38 : 113 – 146 .
  • Keel , M , Smith , H and Sogge , CD . 2002 . Global existence for a quasilinear wave equation outside of star-shaped domains . J. Funct. Anal. , 189 : 155 – 226 .
  • Metcalfe , J and Sogge , CD . 2007 . Global existence of null-form wave equations in exterior domains . Math. Z. , 256 : 521 – 549 .
  • Metcalfe , J and Sogge , CD . 2006 . Global existence for Dirichlet-wave equations with quadratic non-linearities in high dimensions . Math. Ann. , 336 : 391 – 420 .
  • Metcalfe , J and Sogge , CD . 2006 . Long time existence of quasilinear wave equations exterior to star-shaped obstacles via energy methods . SIAM J. Math. Anal. , 38 : 188 – 209 .
  • Metcalfe , J , Nakamura , M and Sogge , CD . 2005 . Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition . Japan. J. Math. , 31 : 391 – 472 .
  • Shibata , Y and Tsutsumi , Y . 1986 . On a global existence theorem of small amplitude solutions for non-linear wave equations in an exterior domain . Math. Z. , 191 : 165 – 199 .
  • Du , Y and Zhou , Y . 2003 . “ The lifespan for non-linear wave eqation outside of star-shaped obstacle in three space dimensions ” . In Comm. Partial Diff. Eqns. (In press)
  • Du , Y , Metcalfe , J , Sogge , CD and Zhou , Yi . 2003 . “ Concerning the strauss conjecture and almost global existence for non-linear Dirichlet-wave equation in 4-dimensions ” . In Comm. Partial Diff. Eqns. (In press)
  • Metcalfe , J and Nakamura , M . 2007 . General quasilinear wave equations with localized dissipation in exterior domains . J. Diff. Eqns. , 233 : 313 – 344 .
  • Nakao , M . 2003 . On global smooth solutions to the initial-boundary value problem for quasilinear wave equations in exterior domains . J. Math. Soc. Japan , 55 : 765 – 795 .
  • Nakao , M . 1998 . Stabilization of local energy in an exterior domain for the wave equation with a localized dissipation . J. Diff. Eqns. , 148 : 388 – 406 .
  • Klainerman , S . 1985 . Uniform decay estimate and the lorentz invariance of the classical wave equations . Comm. Pure and Appl. Math. , 38 : 321 – 332 .
  • Keel , M , Smith , H and Sogge , CD . 2002 . Almost global existence for some semilinear wave equations . J. Anal. Math. , 87 : 265 – 279 .
  • Ta-Tsien , L and Yunmei , C . 1992 . Global Classical Solutions for Non-linear Evolution Equations , UK : Longman Scientific & Technical .
  • Burq , N . 2003 . Global strichartz estimates for nontrapping geometries: about an article by H. Smith and C. Sogge . Comm. Partial Diff. Eqns. , 28 : 1675 – 1683 .

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