Critically and degenerately damped systems of nonlinear wave equations with source terms

References

• Reed , M . 1976 . Abstract Non Linear Wave Equations, Lecture Notes in Mathematics , Berlin : Springer-Verlag .
   Google Scholar
• Agre , K and Rammaha , MA . 2006 . Systems of nonlinear wave equations with damping and source terms . Diff. Integral Eqns. , 19 ( 11 ) : 1235 – 1270 .
   Web of Science ®Google Scholar
• Alves , CO , Cavalcanti , MA , Domingos Cavalcanti , V , Rammaha , MA and Toundykov , D . On existence, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms . in press
   Google Scholar
• Rammaha , MA and Sakuntasathien , S . 2010 . Global existence and blow-up of solutions to systems of nonlinear wave equations with degenerate damping and source terms . Nonlinear Anal. Ser. A Theory Methods Appl. , 72 : 2658 – 2683 .
   Google Scholar
• Barbu , V . 1976 . Nonlinear Differential Equations in Banach Spaces , Leyden : Nordhoff .
   Google Scholar
• Glassey , RT . 1973 . Blow-up theorems for nonlinear wave equations . Math. Z. , 132 : 183 – 203 .
   Web of Science ®Google Scholar
• Levine , HA . 1974 . Instability and nonexistence of global solutions of nonlinear wave equations of the form Pu tt = Au + ℱ( u ) . Trans. Amer. Math. Soc. , 192 : 1 – 21 .
   Web of Science ®Google Scholar
• Payne , LE and Sattinger , D . 1981 . Saddle points and instability of nonlinear hyperbolic equations . Israel Math. J. , 22 : 273 – 303 .
   Google Scholar
• Tsutsumi , H . 1972 . On solutions of semilinear differential equations in a Hilbert space . Math. Japonicea , 17 : 173 – 193 .
   Google Scholar
• Georgiev , V and Todorova , G . 1994 . Existence of a solution of the wave equation with nonlinear damping and source terms . J. Diff. Eqns. , 109 : 295 – 308 .
   Web of Science ®Google Scholar
• Levine , HA and Serrin , J . 1997 . Global nonexistence theorems for quasilinear evolution equations with dissipation . Arch. Rat. Mech. Anal. , 137 : 341 – 361 .
   Web of Science ®Google Scholar
• Pitts , DR and Rammaha , MA . 2002 . Global existence and non-existence theorems for nonlinear wave equations . Indiana Univ. Math. J. , 51 ( 6 ) : 1479 – 1509 .
   Web of Science ®Google Scholar
• Rammaha , MA and Strei , TA . 2002 . Global existence and nonexistence for nonlinear wave equations with damping and source terms . Trans. Amer. Math. Soc. , 354 ( 9 ) : 3621 – 3637 .
   Web of Science ®Google Scholar
• Agre , K and Rammaha , MA . 2001 . Global solutions to boundary value problems for a nonlinear wave equation in high space dimensions . Diff. Integral Eqns. , 14 ( 11 ) : 1315 – 1331 .
   Google Scholar
• Barbu , V , Lasiecka , I and Rammaha , M . 2005 . Existence and uniqueness of solutions to wave equations with nonlinear degenerate damping and source terms . Cont. Cybernetics , 34 ( 3 ) : 665 – 687 .
   Google Scholar
• Barbu , V , Lasiecka , I and Rammaha , M . 2007 . Blow-up of generalized solutions to wave equations with nonlinear degenerate damping and source terms . Indiana Univ. Math. J. , 56 ( 3 ) : 995 – 1022 .
   Web of Science ®Google Scholar
• Adams , RA . 1975 . Sobolev Spaces , New York : Academic Press .
   Google Scholar
• Barbu , V , Lasiecka , I and Rammaha , M . 2005 . On nonlinear wave equations with degenerate damping and source terms . Trans. Amer. Math. Soc. , 357 : 2571 – 2611 .
   Web of Science ®Google Scholar
• Temam , R . 1984 . Navier–Stokes Equations, Theory and Numerical Analysis , New York : North-Holland .
   Google Scholar
• Lions , JL and Magenes , E . 1972 . Non-Homogeneous Boundary Value Problems and Applications I, II , New York, Heidelberg, Berlin : Springer-Verlag .
   Google Scholar