Global Nonexistence for Abstract Evolution Equations with Positive Initial Energy
Global Nonexistence for Abstract Evolution Equations with Positive Initial Energy
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DOI：
10.1006/jdeq.1998.3477
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发表时间：
1998-11
影响因子：
2.4
通讯作者：
P. Pucci;J. Serrin
中科院分区：
文献类型：
--
作者：
P. Pucci;J. Serrin
本文考虑抽象发展方程Put +Q（t）ut +A（t，u）=F（t，u），t∈J=[0，∞）初值问题解的不连续性问题，其中Put + Q（t）ut +A（t，u）是线性自伴算子，A（t，u）和F（t，u）分别是线性算子和非线性驱动力。我们主要关心的是解的不连续性（或爆破）时，初始能量是积极的，但适当的有界。
Abstract In this paper we consider the problem of noncontinuation of solutions of the initial value problem for abstract evolution equations of the form Pu tt +Q(t) u t +A(t, u)=F(t, u), t∈J=[0, ∞), wherePandQare linear self-adjoint operators, andA(t, u) andF(t, u) are respectively a linear operator inu(typically of differential type) and a nonlinear driving force. Our principal concern is the noncontinuation (or blow-up) of solutions when the initial energy is positive, but appropriately bounded.