一类热传导方程第二边值问题的收敛性定理

Convergence Theorem of the Second Boundary Value Problem for a Class of Heat Conduction Equations

该文研究一维抛物型方程第二边值问题的长时间渐近行为.利用经典傅里叶级数的性质证明了一类带热源的热传导方程第二边值问题的解的极限必然是一类平移孤立子,而且这类平移孤立子可以通过求解一类二阶微分方程得到.

The long-time asymptotic behavior of the second boundary value problem of one-dimensional parabolic equation is studied.Using the properties of classical Fourier series,it is proved that the limit of the solution of the second boundary value problem of a class of heat conduction equation with heat source must be a class of translational solitons,and this kind of translational solitons can be obtained by solving a class of second-order differential equations.