The Partial Second Boundary Value Problem of an Anisotropic Parabolic Equation. (2nd May 2019)

• Record Type: Journal Article
• Authors: Zhan, Huashui
• Other Names: Ragusa Maria Alessandra Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2019(2019)
• Publication Date: 2019-05-02
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2019/6930385
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Consider an anisotropic parabolic equation with the variable exponentsv t = ∑ i = 1 n ( b i ( x, t ) v x i p i ( x ) - 2 v x i ) x i + f ( v, x, t ), whereb i ( x, t ) ∈ C 1 ( Q T ¯ ), p i ( x ) ∈ C 1 ( Ω ¯ ), p i ( x ) > 1, b i ( x, t ) ≥ 0, f ( v, x, t ) ≥ 0 . If{ b i ( x, t ) } is degenerate onΓ 2 ⊂ ∂ Ω, then the second boundary value condition is imposed on the remaining part∂ Ω ∖ Γ 2 . The uniqueness of weak solution can be proved without the boundary value condition onΓ 2 .