AI 中文总结
该研究针对3至6维、靶流形为单位球面微小扰动的调和映射热流，构造了稳定自相似爆破解并证明其渐近非线性稳定性，采用类似波映射方程相关问题的摄动方法完成论证。
AI 中文摘要
我们证明了维数为3至6、靶流形为单位球面的微小扰动时，调和映射热流存在稳定自相似爆破。从已知的球面爆破解出发，我们为这类靶流形构造了自相似爆破解，并证明这些解是渐近非线性稳定的。尽管此时球面的爆破解尚未显式知晓，但我们仍可使用类似Donninger、Schörkhuber与作者在文献\uc05b{DonSchWit26}中开发的摄动方法，该文献研究了波映射方程的相关问题。
英文摘要
We prove stable self-similar blowup for the harmonic map heat flow in dimensions 3 to 6 for target manifolds which are slightly perturbed versions of the round sphere. Starting from the known blowup solution for the sphere, we construct self-similar blowup solutions for this class of target manifolds and prove that these solutions are asymptotically nonlinear stable. Although the blowup solution for the sphere is not explicitly known in this case, we can still use perturbative methods similar to those developed by Donninger, Schörkhuber, and the author in \cite{DonSchWit26} who consider a related problem for the wave maps equation.
