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)|
|Number of pages||10|
|Journal||Proceedings of the American Mathematical Society|
|State||Published - 2015|
ASJC Scopus subject areas
- Applied Mathematics