کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4611715 | 1338636 | 2009 | 36 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Finite-dimensional attractors for the quasi-linear strongly-damped wave equation Finite-dimensional attractors for the quasi-linear strongly-damped wave equation](/preview/png/4611715.png)
We present a new method of investigating the so-called quasi-linear strongly-damped wave equations∂t2u−γ∂tΔxu−Δxu+f(u)=∇x⋅ϕ′(∇xu)+g in bounded 3D domains. This method allows us to establish the existence and uniqueness of energy solutions in the case where the growth exponent of the non-linearity ϕ is less than 6 and f may have arbitrary polynomial growth rate. Moreover, the existence of a finite-dimensional global and exponential attractors for the solution semigroup associated with that equation and their additional regularity are also established. In a particular case ϕ≡0ϕ≡0 which corresponds to the so-called semi-linear strongly-damped wave equation, our result allows to remove the long-standing growth restriction |f(u)|⩽C(1+|u|5)|f(u)|⩽C(1+|u|5).
Journal: Journal of Differential Equations - Volume 247, Issue 4, 15 August 2009, Pages 1120–1155