Sub-Gaussian measures and associated semilinear problems (Q427924)

The paper deals with the Markovian Cauchy problem NEWLINE\[NEWLINE\begin{cases}\displaystyle\frac{\partial u}{\partial t}(t)=Lu(t)+\lambda u(t)G\left(\displaystyle\frac{u^2(t)}{\mu(u(t)^2)}\right),\\ u(0)=f,\end{cases}\tag{P}NEWLINE\]NEWLINE where \(L\) is a (linear) Markov generator, \(G\) is a nonlinearity vanishing at one, and \(\mu\) is a probability measure. Under the assumption of \(F\)-Sobolev inequalities, the authors study the existence, uniqueness, some smoothing properties and the long time behaviour of the weak solutions of \((P)\).