On a Parabolic Variational Inequality Related to a Sandpile Problem
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.
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 http://dx.doi.org/10.1007/s10884-013-9320-7
Mathematics and Statistics
Keywords and Phrases
subsolution; supersolution; growth of sandpiles; parabolic variational inequality
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