[PDF] Top 20 Global existence and nonexistence of solutions for quasilinear parabolic equation

... Many natural phenomena have been formulated as the nonlinear diffusive equation (.) such as the model of non-Newton flux in the mechanics of a fluid, the model of a popu- lation, biological species and filtration; ... See full document

... r-Laplacian equation with absorption and nonlinear boundary ...techniques, global existence and blow-up criteria of nonnegative solutions are ... See full document

... The existence and uniqueness of the global solution and blow-up of the solution for () are proved by Wang and Xu ...the global existence and asymptotic behavior of the solution in ... See full document

... assures global existence and decay of the solution energy for arbitrary initial value (see ...of solutions with negative initial energy if r > m (see ...the quasilinear operator – div( |∇ u ... See full document

... Global existence and singularity analyses of the solutions to the nonlinear parabolic equation have been investigated extensively [] and ...of parabolic problems may remain ... See full document

... The rest of this paper is organized as follows. In the next section, we discuss the global existence and nonexistence of solutions, and prove Theorems .-.. Subsequently, in Sects.  and , ... See full document

... a quasilinear wave equation with acoustic bound- ary ...the global existence and regularity of the linear ...the existence, blow-up and decay of solutions for viscoelastic wave ... See full document

... uniform global attractors for multi-valued semiprocesses, we prove the existence of attractors for quasilinear parabolic equations related to Caffarelli-Kohn- Nirenberg inequalities, in which ... See full document

... Here, w denotes the velocity field of the fluid subject to an incompressible Navier-Stokes equation with pressure P and viscosity η, and a gravitational force ∇ φ . In (.), both cells and oxygen are transported ... See full document

... DGH equation via the semigroup approach of quasi- linear hyperbolic equations of evolution and the viscosity ...Camassa-Holm equation. Liu [] and Zhou [] investigated the problems of the existence ... See full document

... the global existence for a parabolic problem in divergence form analogous to ...in parabolic Kato class at infinity P ∞ , the asymptotic behavior of solutions for the problem was studied ... See full document

... In the following, we will derive the estimates 2.10–2.13. The solution is in fact given as limits of smooth solutions of approximate equations see 5, 6, we may assume for our estimates that the solutions ... See full document

... of global existence of our nonlinear reaction diffusion of problem (P), this is done in four steps: the first step we show the positive ...the equation and shows that the problem obtained has a ... See full document

... the set of functions which are continuous in × R and ω-periodic with respect to t. The existence of periodic solutions for parabolic equations has been considered by sev- eral authors; see [–] and ... See full document

... [4] T. Bartsch and M. Willem, “On an Elliptic Equation with Concave and Convex Nonlinearities,” Proceedings of the American Mathematical Society, Vol. 123, 1995, pp. 3555-3561. ... See full document

... Hindawi Publishing Corporation Advances in Difference Equations Volume 2010, Article ID 451619, 11 pages doi 10 1155/2010/451619 Research Article Existence and Nonexistence of Global Solutions of the[.] ... See full document

... which models the self-channeling of a high-power ultrashort laser in matter, see [2, 10]. The existence of positive solutions for (1.5) has been extensively studied recently. In [23], the authors proved ... See full document

... a quasilinear viscoelastic wave equation with acoustic boundary ...a global nonexistence of solutions for a quasilinear viscoelastic wave equation with positive initial ... See full document

... In this paper, we want to address the existence of Eq. (1) with α > 1 2 by using the tech- nique of [5, 19, 20]. Furthermore, we can discuss the exponent p from 2 to 2 ∗ for any N ≥ 3 by introducing different ... See full document

... Positive Solutions of Operator Equations, Noordhoff, Groningen, ...the existence of positive solutions of semilinear elliptic equations, SIAM Review ... See full document