참고문헌
- L. Alfonsi and F.Weissler, Blow up in Rn for a parabolic equation with a damping nonlinear gradient term, Progr. Nonlinear Differential Equations Appl. 7 (1992), 1-20.
- L. Amour and M. Ben-Artzi, Global existence and decay for viscous Hamilton-Jacobi equations, Nonlinear Anal. TMA. 31 (1998), 621-628. https://doi.org/10.1016/S0362-546X(97)00427-6
- J. Bebernes and D. Eberly, Mathematical Problems from Combustion Theory, Applied Mathematical Sciences Series, 83 Springer-Verlag, New York, 1989.
- S. Benachour, S. Dabuleanu, and P. Laurencot, Decay estimates for a viscous Hamilton-Jacobi equation with homogeneous Dirichlet boundary conditions, Asymptotic Anal. 51 (2007), 209-229.
- S. L. Chen, The extinction behavior of solutions for a reaction-diffusion equation, J. Math. Research and Exposition, 18 (1998), 583-586.
- S. L. Chen, The extinction behavior of the solutions for a class of reaction-diffusion equations, Appl. Math. Mech. 22 (2001), 1352-1356.
- M. Chipton and F. B. Weisster, Some blow up results for a nonlinear parabolic equation with a gradient term, SIAM J. Math. Anal. 20 (1989), 886-907. https://doi.org/10.1137/0520060
- L. C. Evans and B. F. Knerr, Instantaneous shrinking of the support of nonnegative solutions to certain nonlinear parabolic equations and variational inequalities, Illinois J. Math. 23 (1979), 153-166.
- I. Fukuda, Extinction and growing-up of solutions of some nonlinear parabolic equations, Transactions of the Kokushikan Univ. Faculty of Engineering, 20 (1987), 1-11.
-
B. H. Gilding, M. Guedda, and R. Kersner, The Cauthy problem for
$u_t={\Delta}u+\left|{\nabla}u\right|^q$ , J. Math. Anal. Appl. 284 (2003), 733-755. https://doi.org/10.1016/S0022-247X(03)00395-0 - Y. G. Gu, Necessary and sufficient conditions of extinction of solution on parabolic equations, Acta. Math. Sin. 37 (1994), 73-79.
-
M. Hesaarki and A. Moameni, Blow-up of positive solutions for a family of nonlinear parabolic equations in general domain in
$R^N$ , Michigan Math. J. 52 (2004), 375-389. https://doi.org/10.1307/mmj/1091112081 - O. A. Ladyzenska, V. A. Solonnikav, and N. N. Vral'tseva, Linear and quasilinear equations of parabolic type, American Mathematical Society, Providence, R. I. 23 (1968), 35-62.
- J. L. Vazquez, The porous medium equation: mathematical theory (Oxford mathematical monographs), Oxford University Press, Oxford, 2006.
- Z. Q. Wu, J. N. Zhao, J. X. Yin, and H. L. Li, Nonlinear diffusion equations, World Scientific, Singapore, 2001.
- S. X. Yang, Extinction of solutions of semilinear heat equations with a gradient term, J. Xiamen University (Natural Science Edition), 35 (1996), 672-676.