µ±Ç°Î»ÖÃ£º Ê×Ò³ > Ñ§Êõ±¨¸æ
Gluing method and blow-up solutions for the energy critical nonlinear heat equation
Ö£ÓÐÈª ¸±½ÌÊÚ(Ìì½ò´óÑ§)
2018-06-28 13:33  ãÉÐÐÊýÑ§Â¥402±¨¸æÌü

ÕªÒª£ºConsidering positive solutions for the fractional heat equation with critical exponent on a smooth bounded domain $\Omega$, we prove the existence of initial datum such that the solution blows up precisely at prescribed distinct points $q_1,\cdots, q_k$ in $\Omega$ as $t\to +\infty$. The main ingredient of the proofs is a new inner-outer gluing scheme for the fractional parabolic problems. We also apply this method in the construction of sign-changing blow-up solutions for the energy critical nonlinear heat equation in large dimensions. These are joint works with Professor Juncheng Wei.