Existence of solution for the n-dimension second order semilinear hyperbolic equations |
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Authors: | Kangqun Zhang |
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Affiliation: | a Department of Mathematics & IMS, Nanjing University, Nanjing 210093, China b Department of Basic Course, Nanjing Institute of Technology, Nanjing 211167, China |
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Abstract: | In the paper we establish the local and global existence of solution for the n-dimensional second order semilinear hyperbolic equation with a strongly singular coefficient which appears in the boundary-value problems of fluid dynamics. Based on the analysis about the loss of regularity on the line t=0 for the solution of the corresponding linear equation and the decay at infinity which caused by the singular coefficient, we obtain the existence of a small solution for the semilinear equation by use of fixed point theorem. |
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Keywords: | Hyperbolic equation Singular coefficient Weighted estimate Existence |
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