Solvability of a semilinear parabolic equation with measures as initial data
Solvability of a semilinear parabolic equation with measures as initial data
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以测量为初始数据的半线性抛物型方程的可解性
DOI：
10.1007/978-3-319-41538-3_15
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Jin Takahashi
中科院分区：
文献类型：
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作者：
Kyoungsuk Jin;Hongmin Seo;Toru Hayashi;Mani Balamurugan; Donghyuk Jeong;Yoo Kyung Go;Jung Sug Hong;Kang Hee Cho;Hirotaka Kakizaki;Nadede Bonnet-Mercier;Min Gyu Kim;Sun Hee Kim;Ryuhei Nakamura;and Ki Tae Nam;Jin Takahashi
本文研究了Cauchy问题可解的一个严格条件，其中，和是上的Radon测度.我们的结果表明，对于某些令人满意的$$\mu（\{y\in \mathbf {R}^N;| X-Y| <\rho \}）\le C\rho ^{N-2/（p-1）}（\log（e+1/\rho））^{-1/（p-1）}$$（，）with a constant.另一方面，如果$$\mu（\{y\in \mathbf {R}^N;| X-Y| <\rho \}）\le C\rho ^{N-2/（p-1）}（\log（e+1/\rho））^{-1/（p-1）-\vareproste}$$（，）with a constant.
We study a sharp condition for the solvability of the Cauchy problem,, where,andis a Radon measure on. Our results show that the problem does not admit any local nonnegative solutions for somesatisfying $$\mu (\{y\in \mathbf {R}^N; |x-y|<\rho \}) \le C\rho ^{N-2/(p-1)}(\log (e+1/\rho ))^{-1/(p-1)}$$ (,) with a constant. On the other hand, the problem admits a local solution if $$\mu (\{y\in \mathbf {R}^N; |x-y|<\rho \}) \le C\rho ^{N-2/(p-1)}(\log (e+1/\rho ))^{-1/(p-1)-\varepsilon }$$ (,) with a constant.