<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet type="text/xsl" href="f1.xsl"?>
<top_article>
 <mrnumber>MR0473550</mrnumber>
 <author>Nakao, Mitsuhiro</author>
 <author_utf8>Mitsuhiro NAKAO</author_utf8>
 <title>Decay of solutions of some nonlinear wave equations in one               space dimension</title>
 <journal>Funkcialaj Ekvacioj. Serio Internacia</journal>
 <volume>20</volume>
 <year>1977</year>
 <page>223--236</page>
 <url_pdf>http://fe.math.kobe-u.ac.jp/FE/Free/vol20/fe20-3-3.pdf</url_pdf>
 <url_infty_pdf>http://fe.math.kobe-u.ac.jp/FE/FE_pdf_with_bookmark/FE11-20-en_KML/fe20-223-236/fe20-223-236.pdf</url_infty_pdf>
 <mathsci_link> http://www.ams.org/mathscinet-getitem?mr=MR0473550</mathsci_link>
<fesi_info>
  <FILE>fe20-223-236</FILE>
  <YEAR>1977</YEAR>
  <TITLE>Decay of Solutions of Some Nonlinear Wave Equations in One Space Dimension</TITLE>
  <AUTHOR>Nakao, Mitsuhiro</AUTHOR>
  <AUTHOR_utf8>Nakao, Mitsuhiro</AUTHOR_utf8>
</fesi_info>

<references>
  <book>
    <bibitem>1</bibitem>
    <author>Amerio, L.; Prouse, G.</author>
    <booktitle>Almost Periodic Functions and Functional Equations</booktitle>
    <publisher>Van Nostrand</publisher>
    <year>1971</year>
    <mr>MR0275061</mr>
    <score>80</score>
    <query_string>Cache/Am/Amerio,Functional,*,1971,1972</query_string>
    <page>viii+184</page>
  </book>

  <article>
    <bibitem>2</bibitem>
    <author>Clements, J. C.</author>
    <title>Existence theorems for some non-linear equations of evolution</title>
    <journal>Canad. J. Math.</journal>
    <vol>22-4</vol>
    <year>1970</year>
    <page>726-745</page>
    <mr>MR0265766</mr>
    <score>100</score>
    <query_string>Cache/Cl/Clements,non-linear,Canad*,1970,1971</query_string>
  </article>

  <fearticle>
    <bibitem>3</bibitem>
    <author>Ebihara, Y.</author>
    <title>On the global classical solutions of nonlinear wave equations</title>
    <journal>Funkcial. Ekvac.</journal>
    <vol>18</vol>
    <year>1975</year>
    <page>227-244</page>
    <mr>MR0415086</mr>
<feart>0415086</feart>
    <score>100</score>
    <query_string>Cache/Eb/Ebihara,classical,Funkcial*,1975,1976</query_string>
  </fearticle>

  <article>
    <bibitem>4</bibitem>
    <author>Levine, H. A.; Murray, A. C.</author>
    <title>Asymptotic behavior and lower bounds for semilinear wave equations in hilbert space with applications</title>
    <journal>SIAM J. Math. Anal.</journal>
    <vol>6-5</vol>
    <year>1975</year>
    <page>846-859</page>
    <mr>MR0381435</mr>
    <score>100</score>
    <query_string>Cache/Le/Levine,applications,SIAM*,1975,1976</query_string>
  </article>

  <book>
    <bibitem>5</bibitem>
    <author>Lions, J. L.</author>
    <booktitle>Qualques M&#233;thods 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>
    <query_string>Cache/Li/Lions,Qualques,*,1969,1970</query_string>
  </book>

  <article>
    <bibitem>6</bibitem>
    <author>Lions, J. L.; Srauss, W. A.</author>
    <title>Some non-linear evolution equations</title>
    <journal>Bull. Soc. Math. France</journal>
    <vol>93</vol>
    <year>1965</year>
    <page>43-96</page>
    <mr>MR0199519</mr>
    <score>100</score>
    <query_string>Cache/Li/Lions,non-linear,Bull*,1965,1966</query_string>
  </article>

  <article>
    <bibitem>7</bibitem>
    <author>Matsumura, A.</author>
    <title>Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equations with the first-order dissipation</title>
    <journal>Publ. RIMS, Kyoto Univ.</journal>
    <vol>13</vol>
    <year>1977/1978</year>
    <page>349-379</page>
    <mr>MR0470507</mr>
    <score>94</score>
    <query_string>Cache/Ma/Matsumura,second-order,Publ*,1976,1977</query_string>
  </article>

  <article>
    <bibitem>8</bibitem>
    <author>Murray, A. C.</author>
    <title>Asymptotic behavior of solutions of hyperbolic inequalities</title>
    <journal>Trans. Amer. Math. Soc.</journal>
    <vol>157</vol>
    <year>1971</year>
    <page>279-296</page>
    <mr>MR0274922</mr>
    <score>100</score>
    <query_string>Cache/Mu/Murray,inequalities,Trans*,1971,1972</query_string>
  </article>

  <article>
    <bibitem>9</bibitem>
    <author>Nakao, M.</author>
    <title>Asymptotic stability of the bounded or almost periodic solution of the wave equation with a nonlinear dissipative term</title>
    <journal>J. Math. Anal. Appl.</journal>
    <vol>58</vol>
    <num>2</num>
    <year>1977</year>
    <page>336-343</page>
    <mr>MR0437890</mr>
    <score>100</score>
    <query_string>Cache/Na/Nakao,dissipative,J*,1977,1978</query_string>
  </article>

  <article>
    <bibitem>10</bibitem>
    <author>Nakao, M.</author>
    <title>Bounded, periodic and almost periodic solutions of the nonlinear hyperbolic partial differential equations</title>
    <journal>J. Differential Equations</journal>
    <vol>23</vol>
    <num>3</num>
    <year>1977</year>
    <page>368-386</page>
    <mr>MR0470428</mr>
    <score>81</score>
    <query_string>Cache/Na/Nakao,hyperbolic,J*,1977,1978</query_string>
  </article>

  <article>
    <bibitem>11</bibitem>
    <author>Nakao, M.</author>
    <title>Convergence of solutions of the wave equation with a nonlinear dissipative term to the steady state</title>
    <journal>Mem. Fac. Sci. Kyushu Univ. Ser. A</journal>
    <ser>A</ser>
    <vol>30</vol>
    <year>1976</year>
    <page>257-265</page>
    <mr>MR0422880</mr>
    <score>100</score>
    <query_string>Cache/Na/Nakao,Convergence,Mem*,1976,1977</query_string>
  </article>

  <article>
    <bibitem>12</bibitem>
    <author>Nakao, M.</author>
    <title>Decay of solutions of some nonlinear evolution equations</title>
    <journal>J. Math. Anal. appl.</journal>
    <vol>60</vol>
    <num>2</num>
    <year>1977</year>
    <page>542-549</page>
    <mr>MR0499564</mr>
    <query_string>Cache/Na/Nakao,solutions,J*,1997,1998</query_string>
  </article>

  <other>
    <bibitem>13</bibitem>
    <raw_data>Nakao, M., Bounded, periodic and almost periodic classical solutions of some nonlinear wave equations with a dissipative term, preprint</raw_data>
    <mr>MR0492914</mr>
  </other>

  <article>
    <bibitem>14</bibitem>
    <author>Ogawa, H.</author>
    <title>Lower bounds for solutions of hyperbolic inequalities</title>
    <journal>Proc. Amer. Math. Soc.</journal>
    <vol>16</vol>
    <year>1965</year>
    <page>853-875</page>
    <mr>MR0193376</mr>
    <score>100</score>
    <query_string>Cache/Og/Ogawa,inequalities,Proc*,1965,1966</query_string>
  </article>

  <article>
    <bibitem>15</bibitem>
    <author>Prodi, G.</author>
    <title>Soluzioni periodiche dell'equazione delle onde contermine dissipativo non lineare</title>
    <journal>Rend. Sem. Mat. Univ. Padova</journal>
    <vol>36</vol>
    <year>1966</year>
    <page>37-49</page>
    <mr>MR0204822</mr>
    <query_string>Cache/Pr/Prodi,dellequazione,Rend*,1966,1967</query_string>
  </article>

  <article>
    <bibitem>16</bibitem>
    <author>Protter, M. H.</author>
    <title>Asymptotic behavior of solutions of hyperbolic inequalities</title>
    <journal>Bull. Amer. Math. Soc.</journal>
    <vol>68</vol>
    <year>1962</year>
    <page>523-525</page>
    <mr>MR0139847</mr>
    <query_string>Cache/Pr/Protter,inequalities,Eull*,1962,1963</query_string>
  </article>

  <article>
    <bibitem>17</bibitem>
    <author>Rabinowitz, P. H.</author>
    <title>Periodic solutions of nonlinear hyperbolic partial differential equations</title>
    <journal>Comm. Pure Appl. Math.</journal>
    <vol>20</vol>
    <year>1967</year>
    <page>145-205</page>
    <mr>MR0206507</mr>
    <query_string>Cache/Ra/Rabinowitz,hyperbolic,Comm*,1969,1970</query_string>
  </article>

  <article>
    <bibitem>17</bibitem>
    <author>Rabinowitz, P. H.</author>
    <title>Periodic solutions of nonlinear hyperbolic partial differential equations, II</title>
    <journal>Comm. Pure Appl. Math.</journal>
    <vol>22</vol>
    <year>1968</year>
    <page>15-39</page>
    <mr>MR0236504</mr>
    <query_string>Cache/Ra/Rabinowitz,hyperbolic,Comm*,1969,1970</query_string>
  </article>

  <article>
    <bibitem>18</bibitem>
    <author>Sather, J.</author>
    <title>Existence of the global classical solutions of the initial-boundary value problem for  $\square u+u^3=f$</title>
    <journal>Arch. Rational Mech. Anal.</journal>
    <vol>22</vol>
    <year>1966</year>
    <page>292-307</page>
    <mr>MR0197965</mr>
    <score>92</score>
    <query_string>Cache/Sa/Sather,initial-boundary,Arch*,1966,1967</query_string>
  </article>

  <article>
    <bibitem>19</bibitem>
    <author>Sattinger, D. H.</author>
    <title>Stability of nonlinear hyperbolic equations</title>
    <journal>Arch. Rational Mech. Anal.</journal>
    <vol>28</vol>
    <year>1968</year>
    <page>226-244</page>
    <mr>MR0224968</mr>
    <score>100</score>
    <query_string>Cache/Sa/Sattinger,hyperbolic,Arch*,1968,1969</query_string>
  </article>

  <book>
    <bibitem>20</bibitem>
    <author>Strauss, W. A.</author>
    <booktitle>Energy Method for Non Linear Partial Differential Equations</booktitle>
    <publisher>Nota di Mat. Brazil</publisher>
    <year>1969</year>
    <mr>MR0273170</mr>
    <score>75</score>
    <query_string>Cache/St/Strauss,Partial,*,1969,1970</query_string>
    <page>ii+154</page>
  </book>

</references>
</top_article>
