<oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:title>Blow-up of generalized solutions to wave equations with nonlinear degenerate damping and source terms</dc:title>
<dc:creator>Viorel Barbu</dc:creator><dc:creator>Irena Lasiecka</dc:creator><dc:creator>Mohammad Rammaha</dc:creator>
<dc:subject>35L05</dc:subject><dc:subject>35L20</dc:subject><dc:subject>58G16</dc:subject><dc:subject>wave equations</dc:subject><dc:subject>damping and source terms</dc:subject><dc:subject>weak solutions</dc:subject><dc:subject>subdifferential</dc:subject><dc:subject>blow-up of solutions</dc:subject><dc:subject>energy estimates</dc:subject>
<dc:description>This article is concerned with the blow-up of \textit{generalized} solutions to the wave equation $u_{tt} - \Delta u + |u|^k j&#39;(u_t) = |u|^{p-1} u$ in $\Omega \times (0,T)$, where $p &gt; 1$ and $ j&#39;$ denotes the derivative of a $C^1$ convex and real valued function $j$. We prove that every generalized solution to the equation that enjoys an additional regularity blows-up in finite time; whenever the exponent $p$ is greater than the critical value $k + m$, and the initial energy is negative.</dc:description>
<dc:publisher>Indiana University Mathematics Journal</dc:publisher>
<dc:date>2007</dc:date>
<dc:type>text</dc:type>
<dc:format>pdf</dc:format>
<dc:identifier>10.1512/iumj.2007.56.2990</dc:identifier>
<dc:source>10.1512/iumj.2007.56.2990</dc:source>
<dc:language>en</dc:language>
<dc:relation>Indiana Univ. Math. J. 56 (2007) 995 - 1022</dc:relation>
<dc:coverage>state-of-the-art mathematics</dc:coverage>
<dc:rights>http://iumj.org/access/</dc:rights>
</oai_dc:dc>