existence and asymptotic expansion of solutions to a nonlinear wave equation with a memory condition at the boundary
Clicks: 121
ID: 219144
2007
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This
article has not been analysed, so there is no overall score —
reader engagement is measured and shown alongside.
Reader Engagement
Steady Performance
30.0
/100
121 views
15 readers
AI Quality Assessment
Not analyzed
Readership in this journal
SteadyRanked #99 of 219 articles by views in icsoft 2006 - 1st international conference on software and data technologies, proceedings
Most read
Least read
Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 219 in total.
Mint this article as an NFT
Not yet mintedCreate a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.
5
SUSD
one-off · no wallet required
Abstract
We study the initial-boundary value problem for the nonlinear wave equation$$displaylines{ u_{tt} - frac{partial }{partial x} (mu ({x,t})u_x ) + K|u |^{p - 2} u + lambda |u_t |^{q - 2} u_t = f(x,t), cr u(0,t) = 0 cr - mu (1,t)u_x (1,t) = Q(t), cr u(x,0) = u_0 (x),quad u_t (x,0) = u_1 (x), cr}$$ where $pgeq 2$, $q geq 2$, $K, lambda$ are given constants and $u_0, u_1, f,mu$ are given functions. The unknown function $u(x,t)$ and the unknown boundary value $Q(t)$ satisfy the linear integral equation$$ Q(t)=K_1(t)u(1,t)+lambda_1(t)u_t(1,t)-g(t)-int_0^t {k(t-s)u(1,s)ds},$$ where $K_1, lambda_1, g, k$ are given functions satisfying some properties stated in the next section. This paper consists of two main sections. First, we prove the existence and uniqueness for the solutions in a suitable function space. Then, for the case $K_1(t)=K_1geq 0$, we find the asymptotic expansion in $K,lambda, K_1$ of the solutions, up to order $N+1$.
| Reference Key |
long2007electronicexistence
Use this key to autocite in the manuscript while using
SciMatic Manuscript Manager or Thesis Manager
|
|---|---|
| Authors | ;Nguyen Thanh Long;Le Xuan Truong |
| Journal | icsoft 2006 - 1st international conference on software and data technologies, proceedings |
| Year | 2007 |
| DOI |
DOI not found
|
| URL | |
| Keywords |
Citations
No citations found. To add a citation, contact the admin at info@scimatic.org
Comments
No comments yet. Be the first to comment on this article.