Higher order energy decay for damped wave equations with variable coefficients

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• 作者：Liqing Lu ; ^{lulq@sxu.edu.cn" class="auth_mail} ; Shengjia Li
• 关键词：Wave equation with variable coefficients ; Linear dissipation ; Riemannian metric ; Distance function of a metric ; Higher order energy
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：1 October 2014
• 年：2014
• 卷：418
• 期：1
• 页码：64-78
• 全文大小：322 K

文摘

Under appropriate assumptions the higher order energy decay rates for the damped wave equations with variable coefficients pan id="mmlsi1" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X14003308&_mathId=si1.gif&_user=111111111&_pii=S0022247X14003308&_rdoc=1&_issn=0022247X&md5=5d846d283b45ae72bf511d4a1cb5f19e" title="Click to view the MathML source">c(x)u_tt−div(A(x)∇u)+a(x)u_t=0pan>pan class="mathContainer hidden">pan class="mathCode">$c(x)u_{tt}-\mathrm{div}(A(x)\mathrm{\nabla }u)+a(x)u_t=0$pan>pan>pan> in pan id="mmlsi2" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X14003308&_mathId=si2.gif&_user=111111111&_pii=S0022247X14003308&_rdoc=1&_issn=0022247X&md5=9bb1093f89d28633855682a45f1732e5" title="Click to view the MathML source">Rⁿpan>pan class="mathContainer hidden">pan class="mathCode">${\mathbb{R}}^n$pan>pan>pan> are established. The results concern weighted (in time) and pointwise (in time) energy decay estimates. We also obtain weighted pan id="mmlsi3" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X14003308&_mathId=si3.gif&_user=111111111&_pii=S0022247X14003308&_rdoc=1&_issn=0022247X&md5=359dfc88291044cc7394c9f0b56ef83d" title="Click to view the MathML source">L²pan>pan class="mathContainer hidden">pan class="mathCode">$L^2$pan>pan>pan> estimates for spatial derivatives.