On the well-posedness of SPDEs with locally Lipschitz coefficients

Mohammud Foondun, Davar Khoshnevisan, Eulalia Nualart

We consider the stochastic partial differential equation, ${\partial }_{t}u=\frac{1}{2}{\partial }_x^{2}u+b(u)+\sigma (u)\dot{W},$ where $u=u(t,x)$ is defined for $(t\,,x)\in(0\,,\infty)\…