Blowup for Nonlocal Nonlinear Diffusion Equations with Dirichlet Condition and a Source. (3rd November 2013)

• Record Type: Journal Article
• Authors: Zhang, Guosheng; Wang, Yifu
• Other Names: Rossi Julio Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-11-03
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/746086
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : This paper is concerned with a nonlocal nonlinear diffusion equation with Dirichlet boundary condition and a source u t ( x, t ) = ∫ - ∞ + ∞ ‍ J (( x - y ) / u ( y, t ) ) d y - u ( x, t ) + u p ( x, t ), x ∈ ( - L, L ), t > 0, u ( x, t ) = 0, x ∉ ( - L, L ), t ≥ 0, and u ( x, 0 ) = u 0 ( x ) ≥ 0, x ∈ ( - L, L ), which is analogous to the local porous medium equation. First, we prove the existence and uniqueness of the solution as well as the validity of a comparison principle. Next, we discuss the blowup phenomena of the solution to this problem. Finally, we discuss the blowup rates and sets of the solution.