| On the Properties of the Solution of a Strongly Degenerate Parabolic Equation |
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| 引用本文： | 程福霞,李锐. On the Properties of the Solution of a Strongly Degenerate Parabolic Equation[J]. 数学季刊, 1996, 0(4) |
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| 作者姓名： | 程福霞 李锐 |
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| 作者单位： | Cheng Fuxia (Department of Applied Mathematics，Tsinghua University，Beijing，100084，China)Li Rui(Department of Mathematics，Kaifeng Teachers College，Kaifeng，475001，China) |
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| 摘 要： | ＯｎｔｈｅＰｒｏｐｅｒｔｉｅｓｏｆｔｈｅＳｏｌｕｔｉｏｎｏｆａＳｔｒｏｎｇｌｙＤｅｇｅｎｅｒａｔｅＰａｒａｂｏｌｉｃＥｑｕａｔｉｏｎＣｈｅｎｇＦｕｘｉａ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉｔ...
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On the Properties of the Solution of a Strongly Degenerate Parabolic Equation |
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| Cheng Fuxia. On the Properties of the Solution of a Strongly Degenerate Parabolic Equation[J]. Chinese Quarterly Journal of Mathematics, 1996, 0(4) |
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| Authors: | Cheng Fuxia |
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| Abstract: | For a strongly degenerate parabolic equation, we first use the results of Ph. Blanc[1] to get that the Neumann problem may not have a global classical solution. The reason is that the gradients of some local classical solutions blow up in finite time. And under some conditions, we get the global integral solution by the use of semigroup. Then, we give a sufficient condition under which the Neumann problem has a global classical solution. Finally. we study the asymptotic behaviour of the classical solution and prove that the solution converges to the mean of the initial value. |
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| Keywords: | strongly degenerate parabolic equation semigroup comparison theorem |
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