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 ...

を考え, 問題(1)の解の定義を与える. $${u = u(x,t)}$$が問題(1)のVery weak solutionであるとは, 次をみたすことである. $${u \in C([0 ...

Abstract: In this paper, we propose Mosaic reduction model using local thermal diffusion equation(MRLTDE) based on local heat diffusion equation and the U-net ...

The forward and backward conditioned diffusion equations relative to the event of the process attaining absorption in one of the boundaries have been derived from the corresponding Kolmogorov ...

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 ...

The ground-level concentration profiles, derived from the analytical solution of the atmospheric diffusion equation for a line source and for the wind speed and vertical dispersion coefficient ...

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...