Abstract
We consider nonlinear parabolic SPDEs of the form ∂tu = − (−Δ)α/2u + b(u) + σ(u)ẇ, where ẇ denotes space-time white noise. The functions b and σ are both locally Lipschitz continuous. Under some suitable conditions on the parameters of this SPDE, we show that the above equation has no random-field solution. This complements recent works of Khoshnevisan and his coauthors.
Original language | English (US) |
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Pages (from-to) | 4085-4094 |
Number of pages | 10 |
Journal | Proceedings of the American Mathematical Society |
Volume | 143 |
Issue number | 9 |
DOIs | |
State | Published - 2015 |
ASJC Scopus subject areas
- Applied Mathematics
- General Mathematics