| （3＋1）维带有源项的反应扩散方程的不变集和精确解 |
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| 引用本文： | 屈改珠,朱春蓉.（3＋1）维带有源项的反应扩散方程的不变集和精确解[J].纯粹数学与应用数学,2009,25(3):579-585. |
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| 作者姓名： | 屈改珠 朱春蓉 |
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| 作者单位： | 屈改珠(渭南师范学院数学系,陕西,渭南,714000);朱春蓉(安徽师范大学数学系,安徽,芜湖,214000) |
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| 基金项目： | 渭南师范学院科研计划项目 |
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| 摘 要： | 讨论了（3＋1）维带有源项的反应扩散方程ut=A1（u）uxx＋A2（u）uyy＋A3（u）uzz＋B1（u）ux^2；＋B2（u）uy^2＋B3（u）uz^2＋Q（u）．通过构建函数不变集的思想方法．得到了上述方程的几个新精确解．该方法也可以用来解N＋1维反应扩散方程．
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| 关 键 词： | 反应扩散方程 不变集 精确解 |
Invariant sets and exact solutions to (3+1)-dimensional reaction-diffusion equations with source term |
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| QU Gai-zhu ,ZHU Chun-rong.Invariant sets and exact solutions to (3+1)-dimensional reaction-diffusion equations with source term[J].Pure and Applied Mathematics,2009,25(3):579-585. |
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| Authors: | QU Gai-zhu ZHU Chun-rong |
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| Institution: | QU Gai-zhu 1,ZHU Chun-rong 2 (1.Department of Mathematics,Weinan Teachers University,Weinan 714000,China,2.Department of Mathematics,Anhui Normal University,Wuhu 241000,China) |
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| Abstract: | (3+1)-dimensional reaction-diffusion equation with source term ut = A1(u)uxx + A2(u)uyy + A3(u)uzz +B1(u)ux2 +B2(u)u2y +B3(u)uz2 +Q(u) is discussed. Using the invariant set, Some special solutions of the above equation are obtained. Using the same approach, exact solutions of the (N +1)-dimensional reaction- diffusion equation will be got. |
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| Keywords: | reaction-diffusion equation invariant sets exact solutions |
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