多重非线性退化的p-Laplacian抛物方程组解的爆破
Blowup of Solutions for a System of Doubly Nonlinear Degenerate Parabolic Equations with p-Laplacian

作者: 齐龙飞 , 苏 璟 , 呼青英 :河南工业大学理学院,河南 郑州;

关键词: 爆破多重非线性抛物方程组Levine凸性方法Blowup of Solution Doubly Nonlinear Parabolic Equations Levine’s Concavity Method

摘要:
本文研究了一类多重非线性退化的p-Laplacian抛物方程组解的爆破,利用修正的Levine凸性方法,在非线性项和初始条件的适当条件下,给出了解爆破时间的下界。

Abstract: This paper is concerned with a system of doubly nonlinear degenerate parabolic equations with p-Laplacian. We prove that, under suitable conditions on the nonlinearity and certain initial datum, the lower bound for the blowup time is given if blowup does occur by using a modification of Levine’s concavity method.

文章引用: 齐龙飞 , 苏 璟 , 呼青英 (2015) 多重非线性退化的p-Laplacian抛物方程组解的爆破。 应用数学进展, 4, 129-135. doi: 10.12677/AAM.2015.42018

参考文献

[1] Ouardi, H.E. (2007) On the finite dimension of attractors of doubly nonlinear parabolic systems with l-trajectories. Archivum Mathematicum, 43, 289-303.

[2] Ouardi, H.E. and Hachimi, A.E. (2001) Existence and attractors of solutions for nonlinear parabolic systems. Electronic Journal of Qualitative Theory of Differential Equations, 2001, 1-16.

[3] Iami, T. and Mochizuki, K. (1991) On the blowup of solutions for quasilinear degenerate parabolic equations. Publications of the Research Institute for Mathematical Sciences, Kyoto University, 27, 695-709.

[4] Levine, H.A. and Sacks, P.E. (1984) Some existence and nonexistence theorems for solutions of degenerate parabolic equations. Journal of Differential Equations, 52, 135-161.

[5] Levine, H.A. and Payne, L.E. (1974) Nonexistence theorems for the heat equations with nonlinear boundary conditions and for the porous medium equation backward in time. Journal of Differential Equations, 16, 319-334.

[6] Levine, H.A., Park, S.R. and Serrin, J.M. (1998) Global existence and nonexistence theorems for quasilinear evolution equations of formally parabolic type. Journal of Differential Equations, 142, 212-229.

[7] Al’shin, A.B., Korpusov, M.O. and Sveshnikov, A.G. (2011) Blow-up in nonlinear Sobolev type equations. De Gruyter, Berlin/New York.

[8] Korpusov, M.O. and Sveshnikov, A.G. (2008) Sufficient close-to-necessary conditions for the blowup of solutions to a strongly nonlinear generalized Boussinesq equation. Computational Mathematics and Mathematical Physics, 48, 1591- 1599.

[9] Polat, N. (2007) Blow up of solution for a nonlinear reaction diffusion equation with multiple nonlinearities. International Journal of Science and Technology, 2, 123-128.

[10] Wang, J. and Ge, Y.Y. (2012) Blow-up analysis for a doubly nonlinear parabolic system with multi-coupled nonlinearities. Electronic Journal of Qualitative Theory of Differential Equations, 2012, 1-17.

[11] Agre, K. and Rammaha, M.A. (2006) Systems of nonlinear wave equations with damping and source terms. Differential and Integral Equations, 19, 1235-1270.

[12] Ball, J.M. (1977) On blowup and nonexistence theorems for nonlinear evolution equations. Quarterly Journal of Ma-thematics: Oxford Journals, 28, 473-486.

[13] Levine, H.A. (1975) Nonexistence of global weak solutions to some properly and improperly posed problem of mathematical physics: The methods of unbounded Fourier coefficients. Mathematische Annalen, 214, 205-220.

[14] Bandle, C. and Brumer, H. (1998) Blowup in diffusion equations: A sur-vey. Journal of Computational and Applied Mathematics, 97, 3-22.

[15] Jiang, Z., Zheng, S. and Song, S. (2004) Blow-up analysis for a nonlinear diffusion equation with nonlinear boundary conditions. Applied Mathematics Letters, 17, 193-199.

[16] Levine, H.A. (1973) Some nonexistence and instability theorems for solutions of formally parabolic equations of the form . Archive for Rational Mechanics and Analysis, 51, 371-386.

[17] Lions, J.L. (1969) Quelques methodes de resolution desproblemes aux limites non lineaires. Dunod, Paris.

[18] Ivanov, A.V. (1993) Quasilinear parabolic equations admitting double degeneracy. St. Petersburg Mathematical Journal, 4, 1153-1168.

[19] Eden, A., Michaux, B. and Rakotoson, J.M. (1991) Doubly nonlinear parabolic type equations as dy-namical systems. Journal of Dynamics and Differential Equations, 3, 87-131.

[20] Laptev, G.I. (1997) Solvability of second-order quasilinear parabolic equations with double degeneration. Siberian Mathematical Journal, 38, 1160-1177.

[21] Tsutsumi, M. (1988) On solution of some doubly nonlinear parabolic equations with absorption. Journal of Mathematical Analysis and Applications, 132, 187-212.

[22] Eden, A. and Rakotoson, J.M. (1994) Expo-nential attractors for a doubly nonlinear equation. Journal of Mathematical Analysis and Applications, 185, 321-339.

[23] Miranville, A. (2006) Finite dimensional global attractor for a class of doubly nonlinear parabolic equation. Central European Journal of Mathematics, 4, 163-182.

[24] Miranville, A. and Zelik, S. (2007) Finite-dimensionality of attractors for degenerate equations of elliptic-parabolic type. Nonlinearity, 20, 1773-1797.

[25] Hachimi, A.E. and Ouardi, H.E. (2002) Existence and of regularity a global attractor for doubly nonlinear parabolic equations. Electronic Journal of Differential Equations, 2002, 1-15.

[26] Ouardi, H.E. and Hachimi, A.E. (2006) Attractors for a class of doubly nonlinear parabolic systems. Electronic Journal of Qualitative Theory of Differential Equations, 2006, 1-15.

[27] Korpusov, M.O. (2013) Solution blow-up for a class of parabolic equations with double nonlinearity. Sbornik: Mathematics, 204, 323-346.

分享
Top