<p>where <spandata-decl="phi"><i>ϕ</i>(<b>r</b>, <i>t</i>) is the <ahref="/wiki/Density"
title="Density">density</a> of the diffusing material <spandata-decl="r"> at location <b>r</b></span>
and <spandata-decl="t"> time <i>t</i></span></span> and
<spandata-decl="Dphir"><i>D</i>(<i>ϕ</i>, <b>r</b>) is the collective <ahref="/wiki/Diffusion_coefficient"class="mw-redirect"title="Diffusion coefficient">diffusion coefficient</a> for density <i>ϕ</i> at location <b>r</b></span>; and ∇ represents the vector <ahref="/wiki/Differential_operator"title="Differential operator">differential operator</a><ahref="/wiki/Del"title="Del">del</a>. If the diffusion coefficient depends on the density then the equation is nonlinear, otherwise it is linear.</p>
<p>More generally, when <i>D</i> is a symmetric <ahref="/wiki/Positive_definite_matrix"class="mw-redirect"title="Positive definite matrix">positive definite matrix</a>, the equation describes <ahref="/wiki/Anisotropy"title="Anisotropy">anisotropic</a> diffusion, which is written (for three dimensional diffusion) as:</p>
<spandata-decl="Dphir"><i>D</i>(<i>ϕ</i>, <b>r</b>) is the collective <a
coefficient">diffusion coefficient</a> for density <i>ϕ</i> at location <b>r</b></span>;
and <spandata-decl="nabla">∇ represents the vector <ahref="/wiki/Differential_operator"title="Differential operator">differential operator</a><ahref="/wiki/Del"title="Del">del</a></span>. If the diffusion coefficient depends on the density then the equation is nonlinear, otherwise it is linear.</p>
<p>More generally, when <spandata-decl="D"><i>D</i> is a symmetric <ahref="/wiki/Positive_definite_matrix"class="mw-redirect"title="Positive definite matrix">positive definite matrix</a></span>, the equation describes <ahref="/wiki/Anisotropy"title="Anisotropy">anisotropic</a> diffusion, which is written (for three dimensional diffusion) as:</p>