The Cauchy-Dirichlet Problem for a Class of Linear Parabolic Differential Equations with Unbounded Coefficients in an Unbounded Domain. (22nd June 2011)

• Record Type: Journal Article
• Authors: Rubio, Gerardo
• Other Names: Stettner Lukasz Academic Editor.
• Is Part Of: International journal of stochastic analysis. Volume 2011(2011)
• Publication Date: 2011-06-22
• Subjects: Stochastic analysis -- Periodicals; Stochastic analysis; Periodicals; 519.22
• DOI: 10.1155/2011/469806
• Languages: English
• ISSNs: 2090-3332

Abstract

Abstract : We consider the Cauchy-Dirichlet problem in[ 0, ∞ ) × D for a class of linear parabolic partial differential equations. We assume thatD ⊂ ℝ d is an unbounded, open, connected set with regular boundary. Our hypotheses are unbounded and locally Lipschitz coefficients, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution to the nonhomogeneous Cauchy-Dirichlet problem using stochastic differential equations and parabolic differential equations in bounded domains.