Weak nonmild solutions to some SPDEs
Weak nonmild solutions to some SPDEs
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某些 SPDE 的弱非温和解
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
D. Khoshnevisan
中科院分区：
文献类型：
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作者：
Daniel Conus;D. Khoshnevisan
我们研究了在初始基准$u_0$是一个（可能有符号的）测度的情况下，由时空白噪声驱动的非线性随机热方程。在这种情况下，不能得到通常意义上的温和随机场解。相反，我们证明了在合适的函数空间中有值的弱解的存在唯一性是可能的。我们的方法是基于通过young型不等式构造随机卷积的广义定义。
We study the nonlinear stochastic heat equation driven by space-time white noise in the case that the initial datum $u_0$ is a (possibly signed) measure. In this case, one cannot obtain a mild random-field solution in the usual sense. We prove instead that it is possible to establish the existence and uniqueness of a weak solution with values in a suitable function space. Our approach is based on a construction of a generalized definition of a stochastic convolution via Young-type inequalities.