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Article

Keywords:
nonlinear wave equations; quenching; convergence; numerical quenching time
Summary:

References:
[1] Abia, L. M., López-Marcos, J. C., Martínez, J.: On the blow-up time convergence of semidiscretizations of reaction-diffusion equations. Appl. Numer. Math. 26 (1998), 399–414. MR 1612360
[2] Boni, T. K.: On quenching of solution for some semilinear parabolic equation of second order. Bull. Belg. Math. Soc. 5 (2000), 73–95. MR 1741748
[3] Boni, T. K.: Extinction for discretizations of some semilinear parabolic equations. C. R. Acad. Sci. Paris Sér. I Math. 333 (8) (2001), 795–800. MR 1868956 | Zbl 0999.35004
[4] Chang, H., Levine, H. A.: The quenching of solutions of semilinear hyperbolic equations. SIAM J. Math. Anal. 12 (1982), 893–903. MR 0635242
[5] Friedman, A., Lacey, A. A.: The blow-up time for solutions of nonlinear heat equations with small diffusion. SIAM J. Math. Anal. 18 (1987), 711–721. MR 0883563 | Zbl 0643.35013
[6] Glassey, R. T.: Blow-up theorems for nonlinear wave equations. Math. Z. 132 (1973), 183–203. MR 0340799 | Zbl 0247.35083
[7] Kaplan, S.: On the growth of solutions of quasi-linear parabolic equations. Comm. Pure Appl. Math. 16 (1963), 305–330. MR 0160044 | Zbl 0156.33503
[8] Keller, J. B.: On solutions of nonlinear wave equations. Comm. Pure Appl. Math. 10 (1957), 523–530. MR 0096889 | Zbl 0090.31802
[9] Levine, H. A.: Instability and nonexistence of global solutions to nonlinear wave equations of the form $\rho u_{tt}=-Av+F(u)$. Trans. Amer. Math. Soc. 192 (1974), 1–21. MR 0344697
[10] Levine, H. A.: Some additional remarks on the nonexistence of global solutions to nonlinear wave equations. SIAM J. Math. Anal. 5 (1974), 138–146. MR 0399682 | Zbl 0243.35069
[11] Levine, H. A.: The quenching solutions of linear parabolic and hyperbolic equations with nonlinear boundary conditions. SIAM J. Math. Anal. 14 (1983), 1139–1153. MR 0718814
[12] Levine, H. A.: The phenomenon of quenching: A survey . Proc. VIth International Conference on Trends in the Theory and Practice of Nonlinear Analysis (Lakshmitanthan, V., ed.), Elservier Nork-Holland, New York, 1985. MR 0817500 | Zbl 0581.35037
[13] Levine, H. A., Smiley, M. W.: The quenching of solutions of linear parabolic and hyperbolic equations with nonlinear boundary conditions. J. Math. Anal. Appl. 103 (1984), 409–427. MR 0718814
[14] Protter, M. H., Weinberger, H. F.: Maximum Principles in Differential Equations. Prentice Hall, Englewood Cliffs, NJ, 1967. MR 0219861
[15] Rammaha, M. A.: On the quenching of solutions of the wave equation with a nonlinear boundary condition. J. Reine Angew. Math. 407 (1990), 1–18. MR 1048525 | Zbl 0698.35088
[16] Reed, M.: Abstract nonlinear wave equations. Lecture Notes in Math., vol. 507, Springer-Verlag Berlin, New-York, 1976. MR 0605679 | Zbl 0319.35060
[17] Sattinger, D. H.: On global solution of nonlinear hyperbolic equations. Arch. Rational Mech. Anal. 30 (1968), 148–172. MR 0227616 | Zbl 0159.39102
[18] Smith, R. A.: On a hyperbolic quenching problem in several dimensions. SIAM J. Math. Anal. 20 (1989), 1081–1094. MR 1009347 | Zbl 0687.35056
[19] Walter, W.: Differential-und Integral-Ungleichungen. Springer, Berlin, 1954.
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