In this paper, we consider the borderline solution to the semilinear equations with critical growth. A concentration phenomenon of the solution when the time goes to infinity is proved. First, we show that a $\varepsilon$-regularity property holds for an $H^1$ solution to the related elliptic equation, and then give a precise description of the formation of the bubbles. A similar bubbling description is also derived for the harmonic maps on surface. (Cf.~Struwe , Qing , Qing-Tian , Chen-Tian , Lin-Wang , and Parker ).
"On partial regularity of the borderline solution of semilinear parabolic equation with critical growth." Adv. Differential Equations 18 (1/2) 147 - 177, January/February 2013. https://doi.org/10.57262/ade/1355867484