Applied Research Frontiers
Title
Existence of Weak Solution with Some Stochastic Hyperbolic Partial Differential Equation
Authors
Osu B. O.*a and Amadi I. U.b
aDepartment of Mathematics, Abia State University, Uturu Abia State, Nigeria.
bDepartment of Mathematics/Statistics Captain Elechi Amadi polytechnic, Rumuola Port Harcourt, Nigeria.
*Corresponding author E-mail address: Osu.bright@mouau.edu.ng (Osu B. O.)
Article History
Publication details: Received: 09th September 2022; Revised: 21st December 2022; Accepted: 21st December 2022; Published: 30th December 2022
Cite this article
Osu B. O.; Amadi I. U. Existence of Weak Solution with Some Stochastic Hyperbolic Partial Differential Equation. Appl. Res. Front., 2022, 1(3), 1-7.
Abstract
The derivatives are well understood in suitable weak sense to make the space complete. Therefore, this paper studied stochastic hyperbolic Partial Differential Equation (PDE) in Sobolev spaces which proffered existence, Uniqueness of weak solution. The smoothness of weak solutions was analyzed to justify our computations. The estimates were logically combined and result showed to follow uniform hyperbolicity condition. To this end, energy estimates showed that the sequences were all bounded.
Keywords
Hyperbolic PDE; weak solutions; stochastic PDE and sobolev spaces
