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Porous Medium Flow with Both a Fractional Potential Pressure and Fractional Time Derivative
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作者 Mark ALLEN luis caffarelli Alexis VASSEUR 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2017年第1期45-82,共38页
The authors study a porous medium equation with a right-hand side. The operator has nonlocal diffusion effects given by an inverse fractional Laplacian operator.The derivative in time is also fractional and is of Capu... The authors study a porous medium equation with a right-hand side. The operator has nonlocal diffusion effects given by an inverse fractional Laplacian operator.The derivative in time is also fractional and is of Caputo-type, which takes into account"memory". The precise model isD_t~αu- div(u(-Δ)^(-σ)u) = f, 0 < σ <1/2.This paper poses the problem over {t ∈ R^+, x ∈ R^n} with nonnegative initial data u(0, x) ≥0 as well as the right-hand side f ≥ 0. The existence for weak solutions when f, u(0, x)have exponential decay at infinity is proved. The main result is H¨older continuity for such weak solutions. 展开更多
关键词 Caputo derivative Marchaud derivative Porous medium equation Hlder continuity Nonlocal diffusion
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