Some Remarks on Global Nonexistence for Nonautonomous Abstract Evolution Equations
Some Remarks on Global Nonexistence for Nonautonomous Abstract Evolution Equations
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DOI：
10.1090/conm/208/02743
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
Howard A. Levine Patrizia Pucci James Serrin
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文献类型：
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作者：
Howard A. Levine Patrizia Pucci James Serrin
本文考虑抽象发展方程Putt + Q（t）ut + A（t，u）= F（t，u），t ∈ J = [0，∞）的初值问题解的不连续性问题，其中P和Q是线性自伴算子，A（t，u）和F（t，u）分别是u中的线性算子（通常是微分型的）和非线性驱动力。我们还考虑了线性耗散Q（t）ut被非线性耗散Q（t，u，ut）代替的情况。这些结果推广了Levine和Levine及Serrin的早期工作。§
In this paper we consider the problem of non-continuation of solutions of the initial value problem for abstract evolution equations of the form Putt + Q(t)ut + A(t, u) = F (t, u), t ∈ J = [0,∞) where P and Q are linear self-adjoint operators, and A(t, u) and F (t, u) are respectively a linear operator in u (typically of differential type) and a nonlinear driving force. We also consider the case in which the linear dissipation, Q(t)ut is replaced by a nonlinear dissipation, Q(t, u, ut). The results extend earlier works of Levine and Levine and Serrin. §