Existence and regularity of the solution of a mixed boundary value problem for the Keldysh equation with a nonlinear absorption term |
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Authors: | Zhonghai Xu Zhenguo FengJiashan Zheng |
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Institution: | a Science College of Northeast Dianli University, Jilin 132013, Chinab School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
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Abstract: | The Keldysh equation is a more general form of the classic Tricomi equation from fluid dynamics. Its well-posedness and the regularity of its solution are interesting and important. The Keldysh equation is elliptic in y>0 and is degenerate at the line y=0 in R2. Adding a special nonlinear absorption term, we study a nonlinear degenerate elliptic equation with mixed boundary conditions in a piecewise smooth domain—similar to the potential fluid shock reflection problem. By means of an elliptic regularization technique, a delicate a priori estimate and compact argument, we show that the solution of a mixed boundary value problem of the Keldysh equation is smooth in the interior and Lipschitz continuous up to the degenerate boundary under some conditions. We believe that this kind of regularity result for the solution will be rather useful. |
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Keywords: | 35J25 35J70 35M12 76N10 |
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