English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We prove existence and smoothness of the density of the solution to anonlinear stochastic heat equation on $L^2(\mathcal{O})$ (evaluated at fixedpoints in time and space), where $\mathcal{O}$ is an open bounded domain in$\mathbb{R}^d$. The equation is driven by an additive Wiener noise and thenonlinear drift term is the superposition operator associated to a realfunction which is assumed to be (maximal) monotone, continuouslydifferentiable, and growing not faster than a polynomial. The proof uses toolsof the Malliavin calculus combined with methods coming from the theory ofmaximal monotone operators.

Existence and regularity of the density for the solution to semilinear dissipative parabolic SPDEs