【摘要】 在一维拟线性热传导方程的Cauchy问题中,当初始条件为不高于二次的多项式函数时,通过Cole-Hopf变换将拟线性方程线性化,利用泊松公式可求解新方程,再逆变换求得原方程的解.更多还原

【Abstract】 In the one- dimensional Cauchy problem of quasilinear heat equation which initial condition is a polynomial function with no more than 2 times.we convert the quasilinear equation into linear one by Cole-Hopf transformation,then we can use Poisson formula to solve the problem.Thus we can gain the solution of the original equation through Cole- Hopf inverse transformation.更多还原