Finite-dimensional attractors for the quasi-linear strongly-damped wave equation
| dc.creator | Kalantarov, Varga | |
| dc.creator | Zelik, Sergey | |
| dc.date | 2008-07-31 | |
| dc.date.accessioned | 2026-07-07T09:54:00Z | |
| dc.date.available | 2026-07-07T09:54:00Z | |
| dc.description | We present a new method of investigating the so-called quasi-linear strongly damped wave equations $$ \partial_t^2u-γ\partial_tΔ_x u-Δ_x u+f(u)= \nabla_x\cdot ϕ'(\nabla_x u)+g $$ 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 $ϕ\equiv0$ which corresponds to the so-called semi-linear strongly damped wave equation, our result allows to remove the long-standing growth restriction $|f(u)|\leq C(1+ |u|^5)$. | |
| dc.description | 36 pages | |
| dc.identifier | https://arxiv.org/abs/0807.5078 | |
| dc.identifier | http://arxiv.org/abs/0807.5078 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166157 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35Q20, 37L30, 73F15 | |
| dc.title | Finite-dimensional attractors for the quasi-linear strongly-damped wave equation | |
| dc.type | text |