The Variational Formulation of the Fokker--Planck Equation | SIAM Journal on Mathematical Analysis

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. https://epubs.siam.org/doi/10.1137/S0036141096303359 Copied! Copying failed. The nonlinear diffusion equation $\rho_t-\Delta(\rho H(\rho-\rho_c))=0$ in $(0,\infty)\times \mathbb{R}^n$, $\rho(0,x)=\rho_0(x)$, where $H$ is the Heaviside function, describes the sandpile model [P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. A (3), pp. 364--374; P. Bantay and I. M. Janosi, Phys. A, 185 (1992), pp. 11--18; R. Cafiero et al., Europhys. Lett., 29 (1995), pp. 111--116] with critical state $\rho_c\in L^\infty(\mathbb{R}^n)\cap L^1(\mathbb{R}^n)$. Here, one proves that a solution $\rho=\rho(t,x)$ can be obtained as the limit of the time-stepping approximation scheme associated with the variational problem $\rho_k={\rm arg}\,\min_{\rho\in\mathcal{P}}\{\frac1h\ d^2(\rho_{k-1},\rho)+\mathbb{E}(\rho)

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. https://epubs.siam.org/doi/10.1137/S0036141096303359 Copied! Copying failed. The nonlinear diffusion equation $\rho_t-\Delta(\rho H(\rho-\rho_c))=0$ in $(0,\infty)\times \mathbb{R}^n$, $\rho(0,x)=\rho_0(x)$, where $H$ is the Heaviside function, describes the sandpile model [P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. A (3), pp. 364--374; P. Bantay and I. M. Janosi, Phys. A, 185 (1992), pp. 1