Energy estimates and variance estimation for hyperbolic stochastic partial differentialequations
Independent thesis Advanced level (professional degree), 30 credits / 45 HE creditsStudent thesis
In this thesis the connections between the boundary conditions and the vari- ance of the solution to a stochastic partial differential equation (PDE) are investigated. In particular a hyperbolical system of PDE’s with stochastic initial and boundary data are considered. The problem is shown to be well- posed on a class of boundary conditions through the energy method. Stability is shown by using summation-by-part operators coupled with simultaneous- approximation-terms. By using the energy estimates, the relative variance of the solutions for different boundary conditions are analyzed. It is concluded that some types of boundary conditions yields a lower variance than others. This is verified by numerical computations.
Place, publisher, year, edition, pages
2011. , 45 p.
IdentifiersURN: urn:nbn:se:liu:diva-70355ISRN: LiTH-MAT-EX--2011/18--SEOAI: oai:DiVA.org:liu-70355DiVA: diva2:438438
Subject / course
2011-08-30, 10:00 (Swedish)
UppsokPhysics, Chemistry, Mathematics