Global solution of the inverse problem for a class of nonlinear evolution equations of dispersive type |
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Authors: | Chen Fang-qi Chen Yu-shu and Wu Zhi-qiang |
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Institution: | (1) Department of Mathematics, Tianjin University, 300072 Tianjin, P R China;(2) Department of Mechanics, Tianjin University, 300072 Tianjin, P R China;(3) Liuhui Center for Applied Mathematics, Nankai University & Tianjin University, 300072 Tianjin, P R China |
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Abstract: | The inverse problem for a class of nonlinear evolution equations of dispersive type was reduced to Cauchy problem of nonlinear
evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence
and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to
the inverse problem discussed here. The existence and uniqueness theorem of global solution was given for this class of nonlinear
evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence
and uniqueness of local solution presented by YUAN Zhong-xin.
Contributed by Chen Yu-shu
Foundation item: the National Natural Science Foundation of China (Significance 199990510); the National Key Basic Research Special Foundation
of China (G1998020316); Liuhui Center for Applied Mathematics, Nankai University & Tianjin University
Biography: Chen Fang-qi (1963-) |
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Keywords: | pseudo-parabolic equation nonlinear evolution equation inverse problem |
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