Here a; bÂ¿0 and pÂ¿1, mÂ¿1. In case of IBVP, in a bounded domain âŠ‚Rn with Dirichlet boundary conditions, the following results are known: 1. When a=0, it is proved (see [1, 3, 8, 14, 16]) that theâ€¦ (More)

We study here instability problems of standing waves for the nonlinear Kleinâ€“Gordon equations and solitary waves for the generalized Boussinesq equations. It is shown that those special waveâ€¦ (More)

We consider the Cauchy problem for the damped nonlinear SchrÃ¶dinger equations, and prove some blowup and global existence results which depend on the size of the damping coefficient. We also discussâ€¦ (More)

In this study we solve the critical exponent problem for the nonlinear wave equation with damping. We show that this critical exponent coincides with the famous Fujita critical exponent for the heatâ€¦ (More)

Article history: Received 29 December 2010 Revised 19 January 2011 Available online 4 February 2011 We prove an abstract version of the striking diffusion phenomenon that offers a strong connectionâ€¦ (More)

We study the asymptotic behavior of energy for wave equations with nonlinear damping g(ut) = |ut|mâˆ’1ut in Rn (n â‰¥ 3) as time t â†’ âˆž. The main result shows a polynomial decay rate of energy under theâ€¦ (More)

We show that the nonlinear wave equation u + ut = 0 is globally well-posed in radially symmetric Sobolev spaces Hk rad(R 3) Ã— Hkâˆ’1 rad (R 3) for all integers k > 2. This partially extends theâ€¦ (More)

From the result of Ginibre and Velo ([9]) the Cauchy problem for (1) is locally wellposed in the energy space X := H1(RN)Ã—L2(RN). Thus for any (u0, u1) âˆˆ X there exists a unique solution ~u := (u,â€¦ (More)

Abstract. Under appropriate assumptions the energy of wave equations with damping and variable coefficients c(x)utt âˆ’ div(b(x)âˆ‡u) + a(x)ut = h(x, t) has been shown to decay. Determining the decayâ€¦ (More)