Acta mathematica scientia,Series A ›› 2000, Vol. 20 ›› Issue (1): 48-57.
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LI Gong-Qing, MA Yi-Chen
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Abstract:
Ｔｈｉｓｐａｐｅｒｓｔｕｄｉｅｓｔｈｅｉｎｖｅｒｓｉｏｎｏｆｔｈｅｎｏｎｌｉｎｅａｒｈｅａｔｓｏｕｒｃｅｆｏｒｈｅａｔｃｏｎｄｕｃｔｉｏｎ ｅｑｕａｔｉｏｎｗｉｔｈａｃｌａｓｓｏｆｎｏｎｌｏｃａｌｂｏｕｎｄａｒｙｆｏｒｔｉｍｅ．ＡｐｐｌｙｉｎｇＳｏｂｏｌｅｖｃｏｍｐａｃｔｍｅｔｈｏｄｓ，ｗｅ＇ｖｅｐｒｏｖｅｄｔｈｅｅｘｉｓｔｅｎｃｅｏｆｔｈｅｈｅａｔｓｏｕｒｃｅｉｎＨ¨ｏｌｄｅｒｓｐａｃｅ．
Key words: Ｈｅａｔｃｏｎｄｕｃｔｉｏｎｅｑｕａｔｉｏｎ, ＩｎｖｅｒｓｅＰｒｏｂｌｅｍ, Ｎｏｎｌｉｎｅａｒｈｅａｔｓｏｕｒｃｅ, Ｈ¨ｏｌｄｅｒ ｓｐａｃｅ．
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LI Gong-Qing, MA Yi-Chen. existence of the nonlinear heat source in an inverse problem arising from heat conduction phenmena [J].Acta mathematica scientia,Series A, 2000, 20(1): 48-57.
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１ ＬｏｒｅｎｚｉＡ．Ａｎｉｎｖｅｒｓｅｐｒｏｂｌｅｍｆｏｒａｓｅｍｉｌｉｎｅａｒｐａｒａｂｏｌｉｃｅｑｕａｔｉｏｎ．Ａｎｎａｌｉｄｉ Ｍａｔｅ，ＰｕｒｅｅｔＡｐｐｌｉｃａ，１９８２，８２（４）：１４５－１６７ ２ ＰｉｌａｎｔＭ，ＲｕｎｄｅｌｌＷ．Ｆｉｘｅｄｐｏｉｎｔｍｅｔｈｏｄｓｆｏｒａｎｏｎｌｉｎｅａｒｐａｒａｂｏｌｉｃｌｎｖｅｒｓｅｃｏｅｆｆｉｃｉｅｎｔｐｒｏｂｌｅｍ．ＣｏｍｍｉｎＰＤＥ，１９８８，１３（４）：４６９－４９３ ３ ＰｉｌａｎｔＭ，ＲｕｎｄｅｌｌＷ．Ｒｅｃｏｖｅｒｙｏｆｏｎｕｎｋｎｏｗｎｓｐｅｃｉｆｉｃｈｅａｔｂｙｍｅａｎｓｏｆｏｖｅｒｐｏｓｅｄｄａｔａ．ＮｕｍｅｒｍｅｔｈｏｄｓｆｏｒＰＤＥ， １９９０，６：１－１６ ４ 李功胜，袁忠信等．热传导方程第三边值非线性热源的反演．郑州大学学报，１９９４，２６（３）：１０－２０ ５ 李功胜，袁忠信．一类特殊边界非线性热源的反演．郑州大学学报，１９９６，２８（４）：１１－１８ ６ ＣａｎｎｏｎＪＲ．Ｔｈｅｏｎｅｄｉｍｅｎｓｉｏｎａｌｈｅａｔｅｑｕａｔｉｏｎ．ＥｎｃｙｃｌｏｐｅｄｉａｏｆＭａｔｈａｎｄｉｔｓＡｐｐｌ．Ｌｏｎｄｏｎ：ＡｄｄｉｓｏｎＷｅｓｌｅｙ，１９８４，２３：５４－５７；３４９－３５１ ７ 布达克Ｂ Ｍ，沙玛尔斯基Ａ Ａ，吉洪诺夫Ａ Ｈ 著．数学物理题解．张石生等译．重庆：科学技术文献出版社重庆分社，１９８２，４７－４９；３２８－３３２ ８ 李开泰，马逸尘．数理方程Ｈｉｌｂｅｒｔ空间方法（上）广义函数和Ｓｏｂｏｌｅｖ 空间．西安：西安交通大学出版社，１９９０，１２３－１４６
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