The Blow up Property of Solutions for Some Pseudoprabolic Equations with Nonlinear Nonlocal Source
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
 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.
 T. W. Ting. Certain non-steady flows of second-order fluids. Archive for Rational Mechanics and Analysis, 1963, 14(1): 1-26.
 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.
 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.
 G. Karch. Asymptotic behavior of solution to some pseudo- parabolic equation. Mathematical Methods in the Applied Scien- ces, 1997, 20(2): 271-289.
 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.
 A. Bouziani. Solvability of nonlinear pseudoparabolic equation with a nonlocal boundary condition. Nonlinear Analysis, 2003, 55(7-8): 883-904.
 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.
 A. Bouziani, N. Merazga. Solution to a semilinear pseudoparabolic problem with integral conditions. Electronic Journal of Differential Equations, 2006, 2006(115): 1-18.
 Pierre. On the maximum principle for pseudoparabolic equations. Indiana University Mathematics Journal, 1981, 30(6): 821-853.
 R. E. Showalter, T. W. Ting. Pseudo-parabolic partial differential equations. SIAM Journal on Mathematic Analysis, 1970, 1(1): 1-26.