On the well-posedness of stochastic partial differential equations with locally Lipschitz coefficients
We consider the stochastic partial differential equation (SPDE) (Formula presented), where u = u(t, x) is defined for (t, x) ∈ (0, ∞ ) × R and Ẇ denotes space-time white noise. We prove that this SPDE is well posed solely under the assumptions that the initial condition u(0) is bounded and measurabl...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2026 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:dnet:recercat____::4e04f92f680b95db58a6896f5101cc4e |
| Online Access: | https://hdl.handle.net/10230/73384 http://dx.doi.org/10.1007/s10959-025-01477-y |
| Access Level: | Open access |
| Keyword: | SPDEs Space-time white noise Existence and uniqueness |
| Summary: | We consider the stochastic partial differential equation (SPDE) (Formula presented), where u = u(t, x) is defined for (t, x) ∈ (0, ∞ ) × R and Ẇ denotes space-time white noise. We prove that this SPDE is well posed solely under the assumptions that the initial condition u(0) is bounded and measurable, and b and σ are locally Lipschitz continuous functions having at most linear growth with regularly behaved local Lipschitz constants. Our method is based on a truncation argument together with moment bounds and tail estimates of the truncated solution. The novelty of our method is in the pointwise nature of the truncation argument. |
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