Global existence of solutions for damped wave equations with nonlinear memory

References

• Todorova , G and Yordanov , B . 2001 . Critical exponent for a nonlinear wave equation with damping . J. Differ. Eqns. , 174 : 464 – 489 .
   Web of Science ®Google Scholar
• Zhang , QS . 2001 . A blow-up result for a nonlinear wave equation with damping: The critical case . C. R. Acad. Sci. Paris Ser. I , 333 : 109 – 114 .
   Web of Science ®Google Scholar
• Nishihara , K . 2003 . L p –L q estimates of solutions to the damped wave equation in 3-dimensional space and their application . Math. Z , 244 : 631 – 649 .
   Web of Science ®Google Scholar
• Narazaki , T . 2004 . L p –L q estimates for damped wave equations and their applications to semi-linear problem . J. Math. Soc. Japan , 56 : 585 – 626 .
   Web of Science ®Google Scholar
• Li , T-T and Zhou , Y . 1995 . Breakdown of solutions to t tt  − ▵u + u t  = |u|1+α . Discrete Contin. Dyn. Syst. , 1 : 503 – 520 .
   Google Scholar
• Li , T-T . 1997 . Nonlinear Heat Conduction with Finite Speed of Propagation, Proceedings of the China-Japan Symposium on Reaction-Diffusion Equations and their Applications and Computational Aspect, Shanghai, 1994 , 81 – 91 . River Edge , , NJ : World Scientific Publishing .
   Google Scholar
• Ikehata , R , Miyaoka , Y and Nakatake , T . 2004 . Decay estimates of solutions for dissipative wave equations in R N with lower power nonlinearities . J. Math. Soc. Japan , 56 : 365 – 373 .
   Web of Science ®Google Scholar
• Ikehata , R and Tanizawa , K . 2005 . Global existence for solutions for semilinear damped wave equation in ℝ n with noncompactly supported initial data . Nonlinear Anal. , 61 : 1189 – 1208 .
   Web of Science ®Google Scholar
• Han , Y and Milani , A . 2000 . On the diffusion phenomenon of quasilinear hyperbolic waves in low space dimensions . Chin. Ann. Math. Ser. B , 21 : 63 – 70 .
   Web of Science ®Google Scholar
• Han , Y and Milani , A . 2000 . On the diffusion phenomenon of quasilinear hyperbolic waves . Bull. Sci. Math. , 124 : 415 – 433 .
   Web of Science ®Google Scholar
• Fino , AZ . 2011 . Critical exponent for damped wave equations with nonlinear memory . Nonlinear Anal. , 74 : 5495 – 5505 .
   Web of Science ®Google Scholar
• Matsumura , A . 1976 . On the asymptotic behavior of solutions of semi-linear wave equations . Publ. RIMS, Kyoto University , 12 : 169 – 189 .
   Google Scholar
• Cui , S . 2001 . Local and global existence of solutions to semilinear parabolic initial value problems . Nonlinear Anal. , 43 : 293 – 323 .
   Web of Science ®Google Scholar