であり, これは$${m}$$の値に応じて次のような名称がついている. $${m=1}$$: 熱方程式(Heat Equation), $${m>1}$$: 多孔質媒質方程式(Porous Medium Equation), $${0 < m < 1}$$: Fast Diffusion Equation, $${m \leqslant 0}$$: Super Fast Diffusion ...

では, 次に$${0 < m < 1}$$の場合であるFast Diffusion Equationの質量保存則を示す. 次の定理がしたがう. Theorem 2(Mass conservation law for the Fast diffusion equation) $${0 < m < 1}$$, $${u_0 \in L^1(\R^N)}$$, $${u_0 \geqslant ...

“However, to compare model predictions with empirical observations, one needs to study the diffusion equation in finite space. Despite the work of illustrious scientists such as Smoluchowski, Pólya, ...

Abstract: In this paper the fractional advection-diffusion equation is analysed with the aim of describing the behavior of water distribution systems. The model is defined by means of a Fractional ...

Numerical simulation of the one-dimensional heat equation using the Crank-Nicolson implicit finite-difference scheme. The solver is implemented in C++ and produces ...