举例说明在二维调和方程的狄利克莱外问题，如对解[tex=2.786x1.286]9iuJszZl4Ix5AKL6+KzDxw==[/tex]不加在无穷远处为有界的限制，那么定解问题的解以不是唯一的 .

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2022-06-19

举例说明在二维调和方程的狄利克莱外问题，如对解[tex=2.786x1.286]9iuJszZl4Ix5AKL6+KzDxw==[/tex]不加在无穷远处为有界的限制，那么定解问题的解以不是唯一的 .

答案：

[b]解[/b]     考虑单位圆外的调和函数，它在园的边界上等于常量1，即[tex=14.0x4.643]fnpmC2J6JmQBLyo5NmGAzwWskHkYW3pO4L9W/DfMamEXcn6IwHXgIHEnwVmxmH9KNg7uglO8itb1tm/W2Y8nGjETqWEoAjPc6+3oTHu7+XjLbBEhYBGMpU8AjcXUhsqk4rv7cHYUUxo+/nk6IFvEZtbriyks4nMFAwHnMq/xe5ZZsOlBtSbylYx5Ymf2fpMpk50KfQcSqKEPlI//A7ME0a1jK7ul7g6+4CcNDKw2kRyR+AwtJ7Ej1hV+9RWpbwVc[/tex]，显然[tex=2.357x1.286]rNVP8p7MuflUkC0syo9IXw==[/tex]是问题的解，又[tex=8.786x2.429]A6fLxIcBdK72w7OfL0CixdSHkS5mXGwI1vbykXffics7PJ60G2XKy/QG7jdSjLbP[/tex]也是问题的解 . 故解不是唯一的 . 

举一反三

内容

0
求下列定解问题的解：[tex=27.143x5.214]fnpmC2J6JmQBLyo5NmGAz+76T2I8QMVR78YL0c5HwWMwa+PHGsEVCOgoI/sqK1gxptSPkHLx/FAesvrVw8SUmkKSE1BVGLIqTpfE8NLRGL3ldsoWxBhw+a4WkFJzZlPL+xX3RFW777xSNOBIzHgNdclEwBhd1eTiToTs5Nt+mGia+x0UvB9fjBmsw0GhBC01h7cGyqE9bscbSXaHOiGPnlBeF2qlxIbIsYEUjMe7LJ8BRIDU9esox5On9J4AIRDH7E80i9Li2qe7O1w3tCjva16ir7TRBqNp3NwiwtL8dPYAR6GCzoMkqWZRaEpMwP9IO2BgoxFvk8cC/Qx977jsKQ==[/tex]
1
求下列定解问题的解：[tex=24.0x3.5]fnpmC2J6JmQBLyo5NmGAz8187g8oz4xFSYH9aJcCY2VS0KqLp7zxAUHvZ3Ge6BD84q8ddQyBeuk+hmbdIUoFqY6qdFSR3VoWz34iY1j6cV0G9foYLkSxqUq2Gg5wugyJJVxKvsjaH67nUgenOeJj7etfWiMbKl7IkgOKM/nH3g1K08c8J1y/OitM207fbzLhvrd87EEWb2EwA8eLrFUA7ForquKisE35QU/ubHHaT9C1LBUDy2Qnsnkz1N507JT5EEGFk85brDvwajrSbuEQbA==[/tex]
2
求下列定解问题的解：[tex=27.143x5.214]fnpmC2J6JmQBLyo5NmGAz+76T2I8QMVR78YL0c5HwWMwa+PHGsEVCOgoI/sqK1gxptSPkHLx/FAesvrVw8SUmkKSE1BVGLIqTpfE8NLRGL3ldsoWxBhw+a4WkFJzZlPL+xX3RFW777xSNOBIzHgNdclEwBhd1eTiToTs5Nt+mGia+x0UvB9fjBmsw0GhBC01h7cGyqE9bscbSXaHOiGPnlBeF2qlxIbIsYEUjMe7LJ8BRIDU9esox5On9J4AIRDH7E80i9Li2qe7O1w3tCjva16ir7TRBqNp3NwiwtL8dPYAR6GCzoMkqWZRaEpMwP9IO2BgoxFvk8cC/Qx977jsKQ==[/tex]
3
求下列定解问题的解：[tex=24.0x3.5]fnpmC2J6JmQBLyo5NmGAz8187g8oz4xFSYH9aJcCY2VS0KqLp7zxAUHvZ3Ge6BD84q8ddQyBeuk+hmbdIUoFqY6qdFSR3VoWz34iY1j6cV0G9foYLkSxqUq2Gg5wugyJJVxKvsjaH67nUgenOeJj7etfWiMbKl7IkgOKM/nH3g1K08c8J1y/OitM207fbzLhvrd87EEWb2EwA8eLrFUA7ForquKisE35QU/ubHHaT9C1LBUDy2Qnsnkz1N507JT5EEGFk85brDvwajrSbuEQbA==[/tex]
4
求下列定解问题的解：[tex=27.143x5.214]fnpmC2J6JmQBLyo5NmGAz+76T2I8QMVR78YL0c5HwWMwa+PHGsEVCOgoI/sqK1gxptSPkHLx/FAesvrVw8SUmkKSE1BVGLIqTpfE8NLRGL3ldsoWxBhw+a4WkFJzZlPL+xX3RFW777xSNOBIzHgNdclEwBhd1eTiToTs5Nt+mGia+x0UvB9fjBmsw0GhBC01h7cGyqE9bscbSXaHOiGPnlBeF2qlxIbIsYEUjMe7LJ8BRIDU9esox5On9J4AIRDH7E80i9Li2qe7O1w3tCjva16ir7TRBqNp3NwiwtL8dPYAR6GCzoMkqWZRaEpMwP9IO2BgoxFvk8cC/Qx977jsKQ==[/tex]