涓浗绉戝闄㈡暟瀛︿笌绯荤粺绉戝鐮旂┒闄㈡湡鍒婄綉

鏁板瀛︽姤 鈥衡�� 2003, Vol. 46 鈥衡�� Issue (6): 1135-114.DOI: 10.12386/A2003sxxb0151

鈥� 璁烘枃 鈥� 涓婁竴绡�    涓嬩竴绡�

甯﹀眬閮ㄩ潪绾挎�у弽搴旈」鐨勯��鍖栨姏鐗╂柟绋嬭В鐨勭垎鐮存�ц川

鍒樺叾鏋�;鏉庣帀绁�;璋㈡槬绾�   

  1. 涓滃崡澶у鏁板绯�,鍗椾含澶у鏁板绯�,鍗椾含澶у鏁板绯� 鍗椾含 210096 ,鍗椾含 210093 ,鍗椾含 210093
  • 鏀剁鏃ユ湡:1900-01-01 淇洖鏃ユ湡:1900-01-01 鍑虹増鏃ユ湡:2003-06-15 鍙戝竷鏃ユ湡:2003-06-15

The Blowup Property of Solutions to Degenerate Parabolic Equation with Localized Nonlinear Reactions

Qi Lin LIU(1),Yu Xiang LI(2),C   

  1. Qi Lin LIU (Department of Mathematics, Southeast University, Nanjing 210096, P. R. China) (E-mail: liuqlseu@yahoo.com.cn) Yu Xiang LI Chun Hong XIE (Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China)
  • Received:1900-01-01 Revised:1900-01-01 Online:2003-06-15 Published:2003-06-15

琚紩娆℃暟

17

鎽樿锛� 鏈枃鐮旂┒甯﹀眬閮ㄩ潪绾挎�у弽搴旈」鐨勯��鍖栨姏鐗╂柟绋嬭В鐨勭垎鐮存�ц川ut=鈻硊m+up(x0,t)-kuq(x,t),鍏朵腑p鈮>0,p>1,01),x0鏄湁鐣屽尯鍩熚╁唴鐨勫浐瀹氱偣,惟(?)RN.鍦ㄤ竴瀹氱殑鍋囪鏉′欢涓�,璇佹槑浜嗚В鍦ㄦ湁闄愭椂鍒荤垎鐮村苟涓旂垎鐮寸偣闆嗘槸鏁翠釜鍖哄煙惟.鍙﹀,濡傛灉瑙(路,t)鏄緞鍚戝绉板嚱鏁颁笖ur鈮�0,鍒欒В鍦ㄦ帴杩戠垎鐮存椂鍒荤殑鐖嗙牬閫熺巼鍦ㄥ尯鍩熚╀笂鏄竴鑷寸殑.鍦ㄨВ鏄潪寰勫悜瀵圭О鐨勬儏鍐典笅,鎴戜滑鐢ㄥ叾浠栨妧宸ц瘉寰楄В鐨勬暣浣撶垎鐮存��.

鍏抽敭璇�: 閫�鍖栨姏鐗╂柟绋�, 鐖嗙牬鐐归泦, 鐖嗙牬閫熺巼

Abstract: In this paper, we investigate the blowup property of solution to degenerate parabolic equations with localized nonlinear reactions where p 鈮� q > 0, p > 1, 0 1) and x0 is a fixed point in the domain 惟(?) RN. We show that under certain conditions the solution blows up in finite time. Moreover, we prove that the set of all blowup points is the whole region. Furthermore, the growth rate of solution near the blowup time is uniform in the domain, provided that u(.,t) are radial functions and ur 鈮� 0. We use other techniques to prove the global blowup in the non-symmetric case.

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