On a Parabolic Variational Inequality Related to a Sandpile Problem

Author

Vy Khoi Le, Missouri University of Science and TechnologyFollow
Klaus Schmitt

Abstract

In this paper, we study the existence of solutions of the variational inequality ⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪∫Qut(v−u)dxdt+∫QΦ(|∇xv(x,t)|)dxdt−∫QΦ(|∇xu(x,t)|)dxdt≥∫Qf(x,t,u(x,t))[v(x,t)−u(x,t)]dxdt,∀v∈K,u∈Kandu(0)=u0, where Q=(0,τ)×Ω and Φ is an N -function. Both coercive and noncoercive cases are considered. We use a topological argument in the coercive case, while a sub-supersolution approach is followed in the noncoercive case.

Recommended Citation

V. K. Le and K. Schmitt, "On a Parabolic Variational Inequality Related to a Sandpile Problem," Journal of Dynamics and Differential Equations, Springer Verlag, Jan 2013.

The definitive version is available at https://doi.org/10.1007/s10884-013-9320-7

Department(s)

Mathematics and Statistics

Keywords and Phrases

subsolution; supersolution; growth of sandpiles; parabolic variational inequality

International Standard Serial Number (ISSN)

1040-7294

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2013 Springer Verlag, All rights reserved.

Publication Date

01 Jan 2013