非线性热传导方程的解和热像法
Solution of Non-Linear Heat Conduction Equation and image Method
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摘要: 文中证明了非线性热传导方程只能有连续解,不可能存在间断解。列出了解非线性热传导方程的一些方法。用热像法给出了平面热波对平面分界面的反射和透射,并证明了热像法的一阶近似性。最后,对激光聚爆氘氚小球,应用高原子序数介质的球壳作为挡过热电子的传播问题作了解释。Abstract: In this paper, the author proves that, for a nonlinear heat conduction equation, there is no discontinuous solution. Some methods of solution for a nonlinear conduction equation are depicted. For a plane interface, the reflection and transmission of a heat wave are given by the method of images. The 1st order of approximation of this method is proved. Lastly, the prevention of superheated electrons is laser implosion of deuterium tritium gas spnere with a shell made of high Z material is interpreted.
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[1] Зелъдович Я.Б.и Ю.П.Райзер,Фuзuка Убарных Волн Высоко-Темnераnурных Гuбообuнамuческuх Яеленuц,Гифмл,Москва(1963). [2] Баренблатт Г.И.,О прибллиженном решении аадач одммериой нестадионанной филътрадии в пористой среде,ПММ,58,(1954),351. [3] Richtmyer, R. D. and K. W. Morton, Difference Methods for Initial Value Problem, 2nd edition, John Wiley and Sons, Inc.(1967). [4] Баренблатт Г.И.,О некоторых неустаоовившихся движеоиях жидкости и газа в пористой среде,ПММ,56,(1952),67. [5] Marshak, R. E., Effect of radiation on shock wave behavior, Phys. of Fluids, Vol. 1,(1958), 24. [6] Spitzer, Jr., L., Physics of Fully Ionized Gases, 2nd edition, New York,(1961). -
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