本文關(guān)鍵詞：一類半線性波方程解在有界區(qū)域中的爆破速率　出處：《東北師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 半線性波方程 爆破速率 能量估計

【摘要】：本文主要研究半線性波方程utt一△u=|u|p-1u初邊值問題解在有界區(qū)域的爆破速率.通過變換ω(s,y)=(T-t)z/p-1 u(t,x),s=1/T-t,將方程轉(zhuǎn)化為另一個波方程,進(jìn)而利用能量估計和爆破分析得出當(dāng)指標(biāo)p1時方程解的爆破速率,最后利用逆變換得到原系統(tǒng)的爆破速率.此外,進(jìn)一步得出當(dāng)或1≤N≤2,1p5時%絬和ut的爆破速率.
[Abstract]:In this paper, we study the blow-up rate of the solution of the semilinear wave equation utt u = u p-1u in a bounded region. The equation is transformed into another wave equation, and the blasting rate of the solution is obtained by energy estimation and blasting analysis. Finally, the blasting rate of the original system is obtained by inverse transformation. In addition, when 1 鈮，

本文編號：1408450