Asymptotic stability and blowing up of solutions of some nonlinear equations
Asymptotic stability and blowing up of solutions of some nonlinear equations
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DOI：
10.1016/0022-0396(77)90196-6
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发表时间：
1977-11
影响因子：
2.4
通讯作者：
H. Ishii
中科院分区：
文献类型：
--
作者：
H. Ishii
本文考虑真实的Hilbert空间H中主要为（wqt）+421（t））-@（u（t））30，f> 0，0.9 u（0）= h（1.2）形式的发展方程.这里，α #和α #是凸下连续（Isc）函数40和4从Hto（-co，+ oo]的次微分，其中y，Z，！J++ t&在[1]中，Brezis研究了问题（II）-（1.2）当a $= 0时解的存在唯一性。最近，Otani [8]给出了保证方程（1.1）-（1.2）整体解存在唯一的充分条件。我们的目的是研究方程（11）-（1.2）解的渐近稳定性和爆破性（即整体解的不存在性），假设θ ~和θ ~分别是度为p和q的（近）齐次函数，2< p< q。这里采用的证明方法是所谓的势阱方法（见[7，9，lo]）。
In this paper, we consider evolution equations mainly of the form (wqt)+% 421 (t))-@(u (t)) 3 0, f> 0, 0.9 u (0)= h(1.2) in a real Hilbert space H. Here 3~ and a# are subdifferentials of convex lower semicontinuous (Isc) functions 40 and 4 from Hto (-co,+ oo] with y, Z,! J++ t& In [l], Brezis studied the existence and uniqueness of solutions of the problem (II)-(1.2) when a $= 0. R A ecently, Otani [8] gave sufficient conditions to ensure existence and uniqueness of global solutions of (1.1)-(1.2). Our purpose is to study asymptotic stability and blowing up (in other words, nonexistence of global solutions) of solutions of (ll)-(1.2) assuming 9~ and+ to be (nearly) homogeneous functions of degreep and q, 2< p< q, respectively. The method of proofs employed here is what is called the potential well method (see [7, 9, lo]).