Abstract
We give new probabilistic results for a class of random two-dimensional homogeneous heat equations with mixed homogeneous Dirichlet and Neumann boundary conditions and an arbitrary initial condition on a rectangular domain. The diffusion coefficient is assumed to be an arbitrary second-order random variable, while the initial condition is a stochastic process admitting a Karhunen-Loève expansion. We then construct pointwise convergent approximations for the main moments and the density of the solution. The theoretical results are numerically illustrated.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
