论文标题
非线性热方程的新寿命结果
New life-span results for the nonlinear heat equation
论文作者
论文摘要
我们获得了非线性热方程最大溶液的存在时间的新估计值，$ \ partial_tu-Δu= | u |^αu，\;α> 0 $，在Lebesgue，加权的Lebesgue空间或测量中具有初始值。考虑了非规范，标志变化以及非多项式衰减初始数据。寿命较低的估计值的证明是基于解决方案的局部结构。上限的证据利用了存在非负溶液的众所周知的必要条件。此外，我们使用扩张方法为寿命建立了新的结果，并为Hardy-Hénon抛物线方程提供了新的寿命估计。
We obtain new estimates for the existence time of the maximal solutions to the nonlinear heat equation $\partial_tu-Δu=|u|^αu,\;α>0$ with initial values in Lebesgue, weighted Lebesgue spaces or measures. Non-regular, sign-changing, as well as non polynomial decaying initial data are considered. The proofs of the lower-bound estimates of life-span are based on the local construction of solutions. The proofs of the upper-bounds exploit a well-known necessary condition for the existence of nonnegative solutions. In addition, we establish new results for life-span using dilation methods and we give new life-span estimates for Hardy-Hénon parabolic equations.
