<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet type="text/xsl" href="f2.xsl"?>
<top_article>
<mrnumber>MR2867017</mrnumber>
<author>Zai-yun ZHANG, Xiu-jin MIAO and De ming YU</author>
<author_utf8>Zai-yun ZHANG, Xiu-jin MIAO and De ming YU</author_utf8>
<title>On Solvability and Stabilization of a Class of Hyperbolic Hemivariational Inequalities in Elasticity</title>
<journal>Funkcialaj Ekvacioj. Serio Internacia</journal>
<volume>54</volume>
<year>2011</year>
<page>297--314</page>
<url_pdf>http://fe.math.kobe-u.ac.jp/FE/FullPapers/54-2/54_297.pdf</url_pdf>
<mathsci_link>http://www.ams.org/mathscinet-getitem?mr=MR2867017</mathsci_link>
<abstract>In this paper we study the existence and stabilization of global weak solutions for a class of second order hyperbolic hemivariational inequalities in elasticity with a discontinuous and nonlinear multi-valued term.</abstract>
<keywords>Weak solutions, Stabilization, Hyperbolic hemivariational inequality.</keywords>
<subject>35L85, 35B40.</subject>
<fesi_info>
  <FILE>54-297</FILE>
  <YEAR>2011</YEAR>
  <TITLE>On Solvability and Stabilization of a Class of Hyperbolic Hemivariational Inequalities in Elasticity</TITLE>
  <AUTHOR>Zai-yun ZHANG, Xiu-jin MIAO and De ming YU</AUTHOR>
  <AUTHOR_utf8>Zai-yun ZHANG, Xiu-jin MIAO and De ming YU</AUTHOR_utf8>
</fesi_info>

<references>

<article>
<bibitem>1</bibitem>
<author>Corr&#234;a, F. J. S. A.; de Menezes, S. B.</author>
<title>Existence of solutions to nonlocal and singular variational elliptic inequality via Galerkin method</title>
<journal>Electron. J. Qual. Theory Differ. Equ.</journal>
<vol>2005</vol>
<year>2005</year>
<page>No.18, 1--12</page>
<mr>MR2164503</mr>
</article>

<article>
<bibitem>2</bibitem>
<author>Gasi&#324;ski, L.; Smolka, M.</author>
<title>Existence of solutions for wave-type hemivariational inequalities with noncoercive viscosity damping</title>
<journal>J. Math. Anal. Appl.</journal>
<vol>270</vol>
<year>2002</year>
<page>150--164</page>
<mr>MR1911757</mr>
</article>

<article>
<bibitem>3</bibitem>
<author>Gasi&#324;ski, L.; Smolka, M.</author>
<title>An existence theorem for wave-type hemivariational inequalities</title>
<journal>Math. Nachr.</journal>
<vol>242</vol>
<year>2002</year>
<page>79--90</page>
<mr>MR1916851</mr>
</article>

<article>
<bibitem>4</bibitem>
<author>Guo, Xing ming</author>
<title>The initial boundary value problem of a mixed-typed hemivariational inequality</title>
<journal>Int. J. Math. Math. Sci.</journal>
<vol>25</vol>
<year>2001</year>
<page>43--52</page>
<mr>MR1812369</mr>
</article>

<article>
<bibitem>5</bibitem>
<author>Medeiros, L. A.</author>
<title>On a new class of nonlinear wave equations</title>
<journal>J. Math. Anal. Appl.</journal>
<vol>69</vol>
<year>1979</year>
<page>252--262</page>
<mr>MR0535295</mr>
</article>

<article>
<bibitem>6</bibitem>
<author>Rivera Rodriguez, P. H.</author>
<title>On local strong solutions of nonlinear partial differential equation</title>
<journal>Applicable Anal.</journal>
<vol>10</vol>
<year>1980</year>
<page>93--104</page>
<mr>MR0575535</mr>
</article>

<article>
<bibitem>7</bibitem>
<author>Kou&#233;mou-Patcheu, S.</author>
<title>On a global solution and asymptotic behaviour for the generalized damped extensible beam equation</title>
<journal>J. Differential Equations</journal>
<vol>135</vol>
<year>1997</year>
<page>299--314</page>
<mr>MR1441273</mr>
</article>

<article>
<bibitem>8</bibitem>
<author>Park, J. Y.; Park, S. H.</author>
<title>Existence and asymptotic stability of solution for hyperbolic differential inclusion with a source term</title>
<journal>J. Inequal. Appl.</journal>
<vol>2007</vol>
<year>2007</year>
<page>Article ID 56350, 1-13</page>
<mr>MR2291652</mr>
</article>

<article>
<bibitem>9</bibitem>
<author>Nakao, M.</author>
<title>A difference inequality and application to nonlinear evolution equations</title>
<journal>J. Math. Soc. Japan</journal>
<vol>30</vol>
<year>1978</year>
<page>747--762</page>
<mr>MR0513082</mr>
</article>

<article>
<bibitem>10</bibitem>
<author>Nakao, M.</author>
<title>Energy decay for the quasilinear wave equation with viscosity</title>
<journal>Math. Z.</journal>
<vol>219</vol>
<year>1995</year>
<page>289--299</page>
<mr>MR1337222</mr>
</article>

<article>
<bibitem>11</bibitem>
<author>Park, J. Y.; Kim, H. M.; Park, S. H.</author>
<title>On weak solutions for hyperbolic differential inclusion with discontinuous nonlinearities</title>
<journal>Nonlinear Anal.</journal>
<vol>55</vol>
<year>2003</year>
<page>103--113</page>
<mr>MR2001634</mr>
</article>

<article>
<bibitem>12</bibitem>
<author>Park, J. Y.; Park, S. H.</author>
<title>On solutions for a hyperbolic systems with differential inclusion and memory source term on the boundary</title>
<journal>Nonlinear Anal.</journal>
<vol>57</vol>
<year>2004</year>
<page>459--472</page>
<mr>MR2064101</mr>
</article>

<article>
<bibitem>13</bibitem>
<author>Jeong, J. M.; Park, J. Y.; Park, S. H.</author>
<title>Hyperbolic hemivariational inequalities with boundary source and damping terms</title>
<journal>Commun. Korean Math. Soc.</journal>
<vol>24</vol>
<year>2009</year>
<page>85--97</page>
<mr>MR2488812</mr>
</article>

<article>
<bibitem>14</bibitem>
<author>Medeiros, L. A.</author>
<title>On a new class of nonlinear wave equations</title>
<journal>J. Math. Anal. Appl.</journal>
<vol>69</vol>
<year>1979</year>
<page>252--262</page>
<mr>MR0535295</mr>
</article>

<book>
<bibitem>15</bibitem>
<author>Teman, R.</author>
<booktitle>Infinite-dimensional dynamics systems in mechanics and physics</booktitle>
<publisher>Applied Mathematical Sciences, 68, Springer-Verlag, NewYork</publisher>
<year>1988</year>
<mr>MR0953967</mr>
</book>

<article>
<bibitem>16</bibitem>
<author>Zhang, Zai-Yun; Liu, Zhen-Hai; Miao, Xiu-Jin</author>
<title>Estimate on the dimension of global attractor for nonlinear dissipative Kirchhoff equation</title>
<journal>Acta Appl. Math.</journal>
<vol>110</vol>
<year>2010</year>
<page>271--282</page>
<mr>MR2601656</mr>
</article>

<article>
<bibitem>17</bibitem>
<author>Gasi&#324;ski, L.; Papageorgiou, N. S.</author>
<title>Nonlinear hemivariational inequalities</title>
<journal>J. Math. Anal. Appl.</journal>
<vol>244</vol>
<year>2000</year>
<page>200--213</page>
<mr>MR1746797</mr>
</article>

<book>
<bibitem>18</bibitem>
<author>Panagiotopoulos, P. D.</author>
<booktitle>Inequality problems in mechanics and applications, convex and nonconvex energy functions</booktitle>
<publisher>Birkh&#228;user, Basel, Boston</publisher>
<year>1985</year>
<mr>MR0896909</mr>
</book>

<book>
<bibitem>19</bibitem>
<author>Panagiotopoulos, P. D.</author>
<booktitle>Hemivariational inequalities, applications in mechanics and engineering</booktitle>
<publisher>Springer-Verlag, NewYork</publisher>
<year>1993</year>
<mr>MR1385670</mr>
</book>

<article>
<bibitem>20</bibitem>
<author>Mig&#243;rski, S.</author>
<title>Evolution hemivariational inequality for a class of dynamic viscoelastic nonmonotone frictional contact problems</title>
<journal>Comput. Math. Appl.</journal>
<vol>52</vol>
<year>2006</year>
<page>677--698</page>
<mr>MR2275558</mr>
</article>

<article>
<bibitem>21</bibitem>
<author>Mig&#243;rski, S.; Ochal, A.</author>
<title>Existence of solutions for second order evolution inclusions with application to mechanical contact problems</title>
<journal>Optimization</journal>
<vol>55</vol>
<year>2006</year>
<page>101--120</page>
<mr>MR2221727</mr>
</article>

<article>
<bibitem>22</bibitem>
<author>Mig&#243;rski, S.; Ochal, A.</author>
<title>A unified approach to dynamic contact problems in viscoelasticity</title>
<journal>J. Elasticity</journal>
<vol>83</vol>
<year>2006</year>
<page>247--275</page>
<mr>MR2248126</mr>
</article>

<book>
<bibitem>23</bibitem>
<author>Adams, R. A.</author>
<booktitle>Sobolev Spaces</booktitle>
<publisher>Pure and Applied Mathematics, 65, Academic Press, New York</publisher>
<year>1975</year>
<mr>MR0450957</mr>
</book>

<book>
<bibitem>24</bibitem>
<author>Lions, J. L.</author>
<booktitle>Quelques M&#233;thodes R&#233;solution des Probl&#232;mes aux Limites Non-Lin&#233;ares</booktitle>
<publisher>Dunod, Paris</publisher>
<year>1969</year>
<mr>MR0259693</mr>
</book>

<book>
<bibitem>25</bibitem>
<author>Yosida, K.</author>
<booktitle>Functional Analysis</booktitle>
<publisher>Springer-Verlag, NewYork</publisher>
<year>1996</year>
<mr>MR1336382</mr>
</book>

<article>
<bibitem>26</bibitem>
<author>Zhang, Zai-Yun; Miao, Xiu-Jin</author>
<title>Global Existence and Uniform Decay for Wave Equation with Dissipative Term and Boundary Damping</title>
<journal>Comput. Math. Appl.</journal>
<vol>59</vol>
<year>2010</year>
<page>1003--1018</page>
<mr>MR2575588</mr>
</article>

</references>
</top_article>
