[PDF] Top 20 Blow up of the Solutions of Nonlinear Wave Equation

... dix of this paper). Therefore, (1 ) has unique nontrivial solution in the set M. Let u be the solution from Theorem 3.1, that is, u is a solution to the integral equation (1 ). From Proposition 2.2, we have that u ... See full document

... weak solutions. Furthermore, we show that there are solutions under some conditions on initial data which blow up in finite time with non-positive initial energy as well as positive initial ... See full document

... r-Laplacian equation with absorption and nonlinear boundary ...and blow-up criteria of nonnegative solutions are ...the blow-up time for the blow-up solution ... See full document

... the blow-up solutions of ...of blow-up ...of blow-up and global existence? What is the limiting behavior of blow-up ... See full document

... of solutions of a parabolic differential equation by blow-up rates”, ...“Regional blow-up and decay of solutions to the Initial-Boundary value problem for u t = uu xx ... See full document

... given nonlinear function. We derive sufficient conditions for the blow-up of the solution to the problem by virtue of an adapted concavity ...weak solutions as well as exponential and uniform ... See full document

... However, in the above papers, the scale invariance plays an important role in the study of the dynamics of blow-up solutions to (1.2); see [7, 10, 12, 14, 18, 20, 21]. Because there exists no scale ... See full document

... where p > 2, ω, μ > 0. The authors established the global existence theorem and proved that the global solution is uniformly bounded. They also constructed the finite time blow- up of solutions ... See full document

... order nonlinear pseudo-parabolic equation with a nonlocal ...a blow-up result of the solutions under suitable assumptions on the initial ... See full document

... global solutions were widely studied in [3, 14, ...the blow-up solutions, a sufficient condition for the existence of blow-up solutions was given by Hebey and Pausader in ... See full document

... for blow-up ...for blow-up time of a system of ...for blow-up time of the solutions to two nonlinear wave ... See full document

... three blow-up results for certain solutions in the case 1): E ( ) 0 < 0 , in the case 2): E ( ) 0 = 0 and in the case 3): E ( ) 0 > 0 ...the blow-up time T ∗− is given for ... See full document

... Ikehata, On global solutions and energy decay for the wave equations of the Kirchhoff type with nonlinear damping terms, J.. Messaoudi, Blow up in a nonlinearly damped wave equation, Mat[r] ... See full document

... time blow-up for solutions starting in the unstable set is proved, but also under some appropriate assumptions on g and the initial data, a blow-up result with positive initial energy ... See full document

... of a solution of problem (.) in the space H reduces the problem to a situation where A – is a compact operator. In Section , we introduce a functional I defined on E whose critical points and weak solutions of ... See full document

... This paper is organized as follows. In Sect. 2, we give material needed for our work. In Sect. 3, we prove the global existence. In Sect. 4, we present some technical lemmas needed in the proof of our result. Section 5 ... See full document

... Degasperis-Procesi equation. The precise blow-up scenarios of strong solutions to the equation are derived by a direct ...the blow-up of strong solutions are ... See full document

... of solutions for the viscoelastic equation, at same time he also obtained a blow-up result with negative ...his blow-up result in ... See full document

... the blow-up problems of the positive solutions to a nonlinear parabolic equation with nonlocal source and nonlocal boundary ...The blow-up and global existence conditions ... See full document

... a blow-up result for solutions with positive initial energy by using the ideas of the ‘potential well’ theory introduced by Payne and Sattinger ...blows up in finite ... See full document