Visco‐elastic damped wave models with time‐dependent coefficient

Halit Sevki Aslan and Michael Reissig

Mathematische Nachrichten, 2024, vol. 297, issue 12, 4535-4581

Abstract: In this paper, we study the following Cauchy problem for linear visco‐elastic damped wave models with a general time‐dependent coefficient g=g(t)$g=g(t)$: ★ utt−Δu−g(t)Δut=0,(t,x)∈(0,∞)×Rn,u(0,x)=u0(x),ut(0,x)=u1(x),x∈Rn.$$\begin{equation} {\begin{cases} u_{tt}- \Delta u {- g(t)\Delta u_t}=0, &(t,x) \in (0,\infty) \times \mathbb {R}^n,\\ u(0,x)= u_0(x),\quad u_t(0,x)= u_1(x), & x \in \mathbb {R}^n. \end{cases}} \end{equation}$$We are interested to study the influence of the damping term −g(t)Δut$-g(t)\Delta u_t$ on qualitative properties of solutions to (★) as decay estimates for energies of higher order and the parabolic effect. The main tools are related to WKB‐analysis. We apply elliptic as well as hyperbolic WKB‐analysis in different parts of the extended phase space.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202300341

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:297:y:2024:i:12:p:4535-4581

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().