CAJ | 학술논문

主要研究了Cauchy问题：{ut=Δu＋up（x）＋uq＋ku,（x,t）∈RN×（0,T） u（x,0）=u0（x）,x∈R{N的非负解的爆破性质,其中01且初值u0（x）充分大时,解u（x,t）在有限时刻爆破;当max{p＋,q}≤1时,解u（x,t）对任意初值u0（x）整体存在;在第4部分,讨论了方程的Fujita指标,并给出了解对任意初值爆破的几种情形.
주요연구료Cauchy문제：{ut=Δu＋up（x）＋uq＋ku,（x,t）∈RN×（0,T） u（x,0）=u0（x）,x∈R{N적비부해적폭파성질,기중01차초치u0（x）충분대시,해u（x,t）재유한시각폭파;당max{p＋,q}≤1시,해u（x,t）대임의초치u0（x）정체존재;재제4부분,토론료방정적Fujita지표,병급출료해대임의초치폭파적궤충정형.
In this paper, we study the blow-up properties for nonnegative solutions to the following Cauchy problem ：{ut=Δu＋up（x）＋uq＋ku,（x,t）∈RN×（0,T） u（x,0）=u0（x）,x∈R{Nhere 0 〈 p = inf p （ x ） ≤p （x）≤ sup p （x） = p ＋ is a nonnegative continuous bounded function and 0 〈 k 〈 A （ where x x A is the first eigenvalue of -A with homogeneous Dirichlet boundary condition）. We prove that there are solutions u（x,t） with blow-up in finite time if and only if max{p＋ ,q} 〉 1 and when initial value Uo（X） is sufficiently big. when max lp ,q I ≤ 1, the solution u（x, t） shows blow-up properties in finite time to any initial value. In Section 4 ,we discuss Fujita indicators of this equation and give several conditions for the solutions blow-up with any initial value.