伪抛物型方程非局部问题解的爆破性
The Blow up Property of Solutions for Some Pseudoprabolic Equations with Nonlinear Nonlocal Source

作者: 江成顺 :中南财经政法大学武汉学院,武汉; 汪先超 :郑州信息科技学院,郑州;

关键词: Blow-Up伪抛物型方程非线性非局部源爆破速率Blow-Up Pseudoparabolic Equation Nonlinear Nonlocal Source Growth Rate

摘要:
本文研究带非线性非局部源项的伪抛物型方程的一类初边值问题。首先证明了模型局部解的存在唯一性,然后证明其解在一定条件下的爆破性质,最后给出两个特殊源项问题解的爆破速率估计。

Abstract:
This paper investigates some Initial Buandary Value Problem (IBVP) of pseudoparabolic equations with nonlinear nonlocal source. Firstly, the authors prove the existence and uniqueness of local solutions of the IBVP. Secondly, authors derive the blow up property of solutions under certain conditions. Finally, they show the growth rate of solutions near the blow up time.

文章引用: 江成顺 , 汪先超 (2011) 伪抛物型方程非局部问题解的爆破性。 理论数学, 1, 80-84. doi: 10.12677/pm.2011.12017

参考文献

[1] B. D. Coleman, W. Noll. Approximation theorem for functionals, with applications in continuum mechanics. Archive for Rational Mechanics and Analysis, 1960, 6(1): 355-370.

[2] T. W. Ting. Certain non-steady flows of second-order fluids. Archive for Rational Mechanics and Analysis, 1963, 14(1): 1-26.

[3] P. J. Chen, M. E. Gurtin. On a theory of heat conduction involving two temperatures. Zeitschrift Fur Angewandte Mathe- matics und Physik, 1968, 19(4): 614-627.

[4] T. B. Benjamin, J. L. Bona, and J. J. Mahony. Model equations for long waves in non-linear dispersive systems. Philosophical Transactions of the Royal Society A, 1972, 272(1220): 47-78.

[5] G. Karch. Asymptotic behavior of solution to some pseudo- parabolic equation. Mathematical Methods in the Applied Scien- ces, 1997, 20(2): 271-289.

[6] A. Elcrat. Coercivity for a third order pseudoparabolic operator with applications to semilinear equations. Journal of Mathe- matical Analysis and Applications, 1977, 61(5): 841-849.

[7] A. Bouziani. Solvability of nonlinear pseudoparabolic equation with a nonlocal boundary condition. Nonlinear Analysis, 2003, 55(7-8): 883-904.

[8] A. Bouziani. Initial-boundary value problems for a class of pseudoparabolic equations with integral boundary conditions. Journal of Mathematical Analysis and Applications, 2004, 291(2): 371-386.

[9] A. Bouziani, N. Merazga. Solution to a semilinear pseudoparabolic problem with integral conditions. Electronic Journal of Differential Equations, 2006, 2006(115): 1-18.

[10] Pierre. On the maximum principle for pseudoparabolic equations. Indiana University Mathematics Journal, 1981, 30(6): 821-853.

[11] R. E. Showalter, T. W. Ting. Pseudo-parabolic partial differential equations. SIAM Journal on Mathematic Analysis, 1970, 1(1): 1-26.

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