Abstract
We consider the stochastic heat equation of the form∂u/∂t=(Δ+Δα)u+(∂f/∂x)(t,x,u)+σ(t,x,u)L˙+W˙H,whereW˙His the fractional noise,L˙is a (pure jump) Lévy space-time white noise,Δis Laplacian, andΔα=-(-Δ)α/2is the fractional Laplacian generator onR, andf,σ:[0,T]×R×R→Rare measurable functions. We introduce the existence and uniqueness of the solution by the fixed point principle under some suitable assumptions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.