Diffusion equation

The diffusion equation is a partial differential equation. In physics, it describes the behavior of the collective motion of micro-particles in a material resulting from the random movement of each micro-particle. In mathematics, it is applicable in common to a subject relevant to the Markov process as well as in various other fields, such as the materials sciences, information science, life science, social science, and so on. These subjects described by the diffusion equation are generally called Brown problems. ∂ ϕ ( r , t ) ∂ t = ∇ ⋅ [ D ( ϕ , r )   ∇ ϕ ( r , t ) ] , {displaystyle {frac {partial phi (mathbf {r} ,t)}{partial t}}= abla cdot {ig },} ∂ ϕ ( r , t ) ∂ t = ∑ i = 1 3 ∑ j = 1 3 ∂ ∂ x i [ D i j ( ϕ , r ) ∂ ϕ ( r , t ) ∂ x j ] {displaystyle {frac {partial phi (mathbf {r} ,t)}{partial t}}=sum _{i=1}^{3}sum _{j=1}^{3}{frac {partial }{partial x_{i}}}left} The diffusion equation is a partial differential equation. In physics, it describes the behavior of the collective motion of micro-particles in a material resulting from the random movement of each micro-particle. In mathematics, it is applicable in common to a subject relevant to the Markov process as well as in various other fields, such as the materials sciences, information science, life science, social science, and so on. These subjects described by the diffusion equation are generally called Brown problems.