Faour, H.; Fino, A. Z.; Jazar, M. Local existence and uniqueness for a semilinear accretive wave equation. (English) Zbl 1213.35309 J. Math. Anal. Appl. 377, No. 2, 534-539 (2011). Summary: We study local existence and uniqueness in the phase space \(H^\pi \times H^{\pi -1}(\mathbb R^N)\) of the solution of the semilinear wave equation \(u_{tt} - \Delta u = u_t|u_t|^{p-1}\) for \(p>1\). Cited in 2 Documents MSC: 35L71 Second-order semilinear hyperbolic equations 35L15 Initial value problems for second-order hyperbolic equations Keywords:wave equations; Strichartz estimates PDFBibTeX XMLCite \textit{H. Faour} et al., J. Math. Anal. Appl. 377, No. 2, 534--539 (2011; Zbl 1213.35309) Full Text: DOI arXiv References: [1] Adams, Robert A., Sobolev Spaces, Pure Appl. Math., vol. 65 (1975), Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers]: Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers] New York, London · Zbl 0314.46030 [2] Bachelot, A., Problème de Cauchy pour des systèmes hyperboliques semi-linéaires, Journées Équations aux dérivées partielles, 1-5 (1983) · Zbl 0536.35051 [3] Cazenave, Thierry; Haraux, Alain, Introduction aux problèmes d’évolution semi-linéaires, Mathématiques & Applications (Paris), vol. 1 (1990), Ellipses: Ellipses Paris · Zbl 0786.35070 [4] Friedman, Avner, Partial Differential Equations of Parabolic Type (1964), Prentice Hall Inc.: Prentice Hall Inc. Englewood Cliffs, NJ · Zbl 0092.31002 [5] Georgiev, Vladimir; Todorova, Grozdena, Existence of a solution of the wave equation with nonlinear damping and source terms, J. Differential Equations, 109, 2, 295-308 (1994) · Zbl 0803.35092 [6] Ginibre, J.; Velo, G., Generalized Strichartz inequalities for the wave equation, J. Funct. Anal., 133, 1, 50-68 (1995) · Zbl 0849.35064 [7] Haraux, A., Remarks on the wave equation with a nonlinear term with respect to the velocity, Port. Math., 49, 4, 447-454 (1992) · Zbl 0782.35042 [8] Haraux, A.; Zuazua, E., Decay estimates for some semilinear damped hyperbolic problems, Arch. Ration. Mech. Anal., 100, 2, 191-206 (1988) · Zbl 0654.35070 [9] Hosono, Takafumi; Ogawa, Takayoshi, Large time behavior and \(L^p-L^q\) estimate of solutions of 2-dimensional nonlinear damped wave equations, J. Differential Equations, 203, 1, 82-118 (2004) · Zbl 1049.35134 [10] Jazar, M.; Kiwan, R., Blow-up results for some second-order hyperbolic inequalities with a nonlinear term with respect to the velocity, J. Math. Anal. Appl., 327, 12-22 (2007) · Zbl 1111.35138 [11] Kopáčková, M., Remarks on bounded solutions of a semilinear dissipative hyperbolic equation, Comment. Math. Univ. Carolin., 30, 4, 713-719 (1989) · Zbl 0707.35026 [12] Messaoudi, Salim A., Blow up and global existence in a nonlinear viscoelastic wave equation, Math. Nachr., 260, 58-66 (2003) · Zbl 1035.35082 [13] Nishihara, Kenji, \(L^p-L^q\) estimates of solutions to the damped wave equation in 3-dimensional space and their application, Math. Z., 244, 3, 631-649 (2003) · Zbl 1023.35078 [14] Shatah, Jalal; Struwe, Michael, Geometric Wave Equations, Courant Lect. Notes Math., vol. 2 (1998), New York University Courant Institute of Mathematical Sciences, viii+153 pp · Zbl 0993.35001 [15] Strichartz, Robert S., Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J., 44, 3, 705-714 (1977) · Zbl 0372.35001 [16] Triebel, Hans, Theory of Function Spaces, Monogr. Math., vol. 78 (1983), Birkhäuser Verlag: Birkhäuser Verlag Basel · Zbl 0546.46028 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.