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<mrnumber>MR1865394</mrnumber>
<author>Mohammed AASSILA and Abbes BENAISSA</author>
<author_utf8>Mohammed AASSILA and Abbes BENAISSA</author_utf8>
<title>Existence Globale et Comportement Asymptotique des Solutions des Equations de Kirchhoff Moyennement Degenerees avec un Terme Non-Lineaire Dissipatif</title>
<journal>Funkcialaj Ekvacioj. Serio Internacia</journal>
<volume>44</volume>
<year>2001</year>
<page>309--333</page>
<url_pdf>http://fe.math.kobe-u.ac.jp/FE/FullPapers/vol44/fe44-2-7.pdf</url_pdf>
<mathsci_link>http://www.ams.org/mathscinet-getitem?mr=MR1865394</mathsci_link>
<fesi_info>
  <FILE>44-309</FILE>
  <YEAR>2001</YEAR>
  <TITLE>Existence Globale et Comportement Asymptotique des Solutions des &#201;quations de Kirchhoff Moyennement D&#233;g&#233;n&#233;r&#233;es avec un Terme Non-Lin&#233;aire Dissipatif</TITLE>
  <AUTHOR>Mohammed AASSILA and Abbes BENAISSA</AUTHOR>
  <AUTHOR_utf8>Mohammed AASSILA and Abbes BENAISSA</AUTHOR_utf8>
</fesi_info>

<references>

<article>
<bibitem>1</bibitem>
<author>Aassila, M.</author>
<title>Global existence and decay properties of solutions to degenerate wave equattons with dissipative terms</title>
<journal>Bulletin of the Australian Math. Soc.</journal>
<vol>60</vol>
<year>1999</year>
<page>1-10</page>
<mr>MR1702858</mr>
</article>

<article>
<bibitem>2</bibitem>
<author>Aassila, M.</author>
<title>A new approach of strong stabilization of distributed systems</title>
<journal>Differential and Integral Equations</journal>
<vol>11</vol>
<year>1998</year>
<page>369-376</page>
<mr>MR1741852</mr>
</article>

<article>
<bibitem>3</bibitem>
<author>Aassila, M.</author>
<title>Asymptoyic behavior of solutions to a quasilinear hyperbolic equation with nonlinear damping</title>
<journal>EJQTDE</journal>
<vol>1998</vol>
<year>1998</year>
<page>1-12</page>
<mr>MR1641078</mr>
</article>

<article>
<bibitem>4</bibitem>
<author>Arosio, A.</author>
<title>Linear second order differential equations in Hilbert spaces: The Cauchy problem and asymptotic behavior for large time</title>
<journal>Archiv for Rational Mechanics and Analysis</journal>
<vol>86</vol>
<year>1984</year>
<page>147-180</page>
<mr>MR0751306</mr>
</article>

<article>
<bibitem>5</bibitem>
<author>Arosio, A.</author>
<title>Averaged evolution equations. The Kirchhoff string and its treatement in scales of Banach spaces</title>
<journal>Proceeding of the "2nd workshop on functional-analytic methods in complex analysis" (Trieste, 1993), World Scientific, Singapore</journal>
<year>1995</year>
<page>220-254</page>
<mr>MR1414220</mr>
</article>

<article>
<bibitem>6</bibitem>
<author>Arosio, A.; Garavaldi, S.</author>
<title>On the mildly degenerate Kirchhoff String</title>
<journal>Mathematical Methods in the Applied Sciences</journal>
<vol>14</vol>
<year>1991</year>
<page>177-195</page>
<mr>MR1099324</mr>
</article>

<article>
<bibitem>7</bibitem>
<author>Arosio, A.; Spagnolo, S.</author>
<title>Global solutions to the Cauchy problem for a nonlinear hyperbolic equation</title>
<journal>in "Nonlinear P. D. E. and Their Appliquation", vol. VI, Coll&#232;ge de France, Seminar, Research Notes Math. Vol. 109, Eds H. Brezis and J. L. Lions, Pitman, Boston</journal>
<year>1984</year>
<page>1-26</page>
<mr>MR0772234</mr>
</article>

<article>
<bibitem>8</bibitem>
<author>Crippa, H. R.</author>
<title>On local solutions of some mildly degenerate hyperbolic equations</title>
<journal>Nonlinear Analysis</journal>
<vol>21</vol>
<year>1993</year>
<page>565-574</page>
<mr>MR1245862</mr>
</article>

<article>
<bibitem>9</bibitem>
<author>D'Ancona, P.; Spagnolo, S.</author>
<title>Global solvability for the degenerate Kirchhoff equation with real analytic data</title>
<journal>Invent. Math.</journal>
<vol>108</vol>
<year>1992</year>
<page>247-262</page>
<mr>MR1161092</mr>
</article>

<article>
<bibitem>10</bibitem>
<author>Dix, J. G.</author>
<title>Decay of solutions of a degenerate hyperbolic equation</title>
<journal>Electronic Journal of Differential Equations</journal>
<vol>1998</vol>
<year>1998</year>
<page>1-10</page>
<mr>MR1637075</mr>
</article>

<book>
<bibitem>11</bibitem>
<author>Dixmier, J.</author>
<booktitle>Les alg&#232;bres d'op&#233;rateurs dans l'espace Hilbertien</booktitle>
<publisher>Gauthier-Villars, Paris</publisher>
<year>1957</year>
<mr>MR0094722</mr>
</book>

<article>
<bibitem>12</bibitem>
<author>Ebihara, Y.; Medeiros, L. A.; Miranda, M. M.</author>
<title>Local solutions for nonlinear degenerate hyperbolic equation</title>
<journal>Nonlinear Analysis</journal>
<vol>10</vol>
<year>1986</year>
<page>27-40</page>
<mr>MR0820656</mr>
</article>

<other>
<bibitem>13</bibitem>
<raw_data>Ghisi, M. and Gobbino, M., Global existence for mildly degenerate dissipative hyperbolic equation of Kirchhoff type, Preprint Dip. Mat. Univ. Pisa (December 1997)</raw_data>
</other>

<article>
<bibitem>14</bibitem>
<author>Gourdin, D.; Mechab, M.</author>
<title>Probl&#232;me de Goursat non 1in&#233;aire dans les classes de Gevrey, pour des &#233;quations de Kirchhoff g&#233;n&#233;ralis&#233;es</title>
<journal>J. Math. Pures Appl.</journal>
<vol>75</vol>
<year>1996</year>
<page>569-593</page>
<mr>MR1423048</mr>
</article>

<article>
<bibitem>15</bibitem>
<author>Hosoya, M.; Yamada, Y.</author>
<title>On some nonlinear wave equations II: global existence and energy decay of solutions</title>
<journal>J. Fac. Sci. Univ. Tokyo Sect. IA Math.</journal>
<vol>38</vol>
<year>1991</year>
<page>239-250</page>
<mr>MR1127082</mr>
</article>

<article>
<bibitem>16</bibitem>
<author>Ikehata, R.; Okazawa, N.</author>
<title>A class of second order quasilinear evolution equations</title>
<journal>Journal of Differential equations</journal>
<vol>114</vol>
<year>1994</year>
<page>106-131</page>
<mr>MR1302137</mr>
</article>

<book>
<bibitem>17</bibitem>
<author>Kirchhoff, G.</author>
<booktitle>Vorlesungen &#252;ber Mechartik</booktitle>
<publisher>Leipzig, Teubner</publisher>
<year>1883</year>
</book>

<book>
<bibitem>18</bibitem>
<author>Lions, J. L.</author>
<booktitle>Quelques m&#233;thodes de r&#233;solution des probl&#232;mes aux limites non-lin&#233;aires</booktitle>
<publisher>Dunod, Paris</publisher>
<year>1969</year>
<mr>MR0259693</mr>
</book>

<article>
<bibitem>19</bibitem>
<author>Lions, J. L.</author>
<title>On some questions in boundary value problem of mathematical physics</title>
<journal>in Contemporary Developments in Cont. Mech. and P. D. E, G. M. de la Penha, L. A. Medetros eds</journal>
<year>1978</year>
<page>284-346</page>
<mr>MR0519648</mr>
</article>

<book>
<bibitem>20</bibitem>
<author>Lions, J. L.; Magenes, E.</author>
<booktitle>Non homogenous boundary value problems and applications</booktitle>
<publisher>Dunod, 1 (1970), Springer</publisher>
<year>1972</year>
<mr>MR0350178</mr>
</book>

<article>
<bibitem>21</bibitem>
<author>Matos, M. P.</author>
<title>Mathematical analysis of the nonlinear model for the vibrations of a string</title>
<journal>Nonlinear Analysis</journal>
<vol>17</vol>
<year>1991</year>
<page>1125-1137</page>
<mr>MR1137898</mr>
</article>

<fearticle>
<bibitem>22</bibitem>
<author>Matos, M. P.; Pereira, D. C.</author>
<title>On a hyperbolic equation with strong damping</title>
<journal>Funkcialaj Ekvacioj</journal>
<vol>34</vol>
<year>1991</year>
<page>303-311</page>
<mr>MR1130466</mr>
<feart>1130466</feart>
</fearticle>

<article>
<bibitem>23</bibitem>
<author>Matsuyama, T.</author>
<title>Quasilinear hyperbolic-hyperbolic singular perturbations with nonmonotone nonlinearity</title>
<journal>Nonlinear Analysis</journal>
<vol>35</vol>
<year>1999</year>
<page>589-607</page>
<mr>MR1656926</mr>
</article>

<article>
<bibitem>24</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>25</bibitem>
<author>Menzala, G. P.</author>
<title>On classical solutions of a quasilinear hyperbolic equation</title>
<journal>Nonlinear Analysis</journal>
<vol>3</vol>
<year>1979</year>
<page>613-627</page>
<mr>MR0541872</mr>
</article>

<article>
<bibitem>26</bibitem>
<author>Medeiros, L. A.; Miranda, M.</author>
<title>Solutions for the equations of nonlinear vibrations in Sobolev spaces of fractionary order</title>
<journal>Computational Applied Math.</journal>
<vol>6</vol>
<year>1987</year>
<page>257-276</page>
<mr>MR0935676</mr>
</article>

<article>
<bibitem>27</bibitem>
<author>Mizumachi, T.</author>
<title>Time decay of solutions to degenerate Kirchhoff type equation</title>
<journal>Nonlinear Analysis</journal>
<vol>33</vol>
<year>1998</year>
<page>235-252</page>
<mr>MR1617984</mr>
</article>

<article>
<bibitem>28</bibitem>
<author>Nakao, M.</author>
<title>A difference inequality and its applications to nonlinear evolution equations</title>
<journal>J. Math. Soc. Japan</journal>
<vol>30</vol>
<year>1978</year>
<page>141-762</page>
<mr>MR0513082</mr>
</article>

<fearticle>
<bibitem>29</bibitem>
<author>Nishihara, K.; Yamada, Y.</author>
<title>On global solutions of some degenerate quasilinear hyperbolic equations with dissipative terms</title>
<journal>Funkcialaj Ekvacioj</journal>
<vol>33</vol>
<year>1990</year>
<page>151-159</page>
<mr>MR1065473</mr>
<feart>1065473</feart>
</fearticle>

<fearticle>
<bibitem>30</bibitem>
<author>Ono, K.</author>
<title>Global existence and decay properties of solutions of some mildly degenerate nonlinear dissipative Kirchhoff strings</title>
<journal>Funkcialaj Ekvacioj</journal>
<vol>40</vol>
<year>1997</year>
<page>255-270</page>
<mr>MR1480278</mr>
<feart>1480278</feart>
</fearticle>

<article>
<bibitem>31</bibitem>
<author>Pohozaev, S. I.</author>
<title>On a class of quasilinear hyperbolic equations</title>
<journal>Math. Sbornik</journal>
<vol>96</vol>
<year>1975</year>
<page>145-158</page>
<mr>MR0369938</mr>
</article>

<article>
<bibitem>32</bibitem>
<author>Riviera Rodriguez, P. H.</author>
<title>On local strong solution of a nonlinear partial differential equation</title>
<journal>Appl. Anal.</journal>
<vol>10</vol>
<year>1980</year>
<page>93-104</page>
<mr>MR0575535</mr>
</article>

<article>
<bibitem>33</bibitem>
<author>Spagnolo, S.</author>
<title>The Cauchy problem for Kirchhoff equations</title>
<journal>Rendiconti del Seminario Matematico e Fisico Di Milano</journal>
<vol>LXII</vol>
<year>1992</year>
<page>17-51</page>
<mr>MR1293773</mr>
</article>

<book>
<bibitem>34</bibitem>
<author>Temam, R.</author>
<booktitle>Infinite-dimensional dynamical systems in mechanics and physics</booktitle>
<publisher>Applied Mathematical Sciences, 68, Springer-Verlag, New York</publisher>
<year>1988</year>
<mr>MR0953967</mr>
</book>

<article>
<bibitem>35</bibitem>
<author>Tsutsumi, M.</author>
<title>On solutions of some semilinear differential equations in a Hilbert space</title>
<journal>Math. Japonica</journal>
<vol>17</vol>
<year>1972</year>
<page>173-193</page>
<mr>MR0355247</mr>
</article>

<article>
<bibitem>36</bibitem>
<author>Yamada, Y.</author>
<title>Some nonlinear degenerate wave equations</title>
<journal>Nonlinear Anal.</journal>
<vol>11</vol>
<year>1987</year>
<page>1155-1168</page>
<mr>MR0913675</mr>
</article>

<fearticle>
<bibitem>37</bibitem>
<author>Yamazaki, T.</author>
<title>On local solution of some quasilinear degenerate hyperbolic equations</title>
<journal>Funkcialaj Ekvacioj</journal>
<vol>31</vol>
<year>1988</year>
<page>439-457</page>
<mr>MR0987797</mr>
<feart>0987797</feart>
</fearticle>

</references>
</top_article>
