Mathematics

Mathematics related to stubs.

Multi-Dimensional Reaction-Diffusion Equations

Volumetric partial differential equations

\[\begin{split}\partial_t u^{(a)}_{i} &= \nabla \cdot (D^{(a)}_{i} \nabla u^{(a)}_{i}) + f^{(a)}_{i}(u^{(a)}) ~~\text{in}~~ \Omega^{(a)}\\ D^{(a)}_{i} (\nabla u^{(a)}_{i} \cdot n) &= r^{(abc)}_{i}(u^{(a)}, u^{(b)}, v^{(abc)}) ~~\text{on}~~ \Gamma^{(abc)}\end{split}\]

Surface partial differential equations

\[\begin{split}\partial_t v^{(abc)}_{i} &= \nabla_S \cdot (D^{(abc)}_{i} \nabla_S v^{(abc)}_{i}) + g^{(abc)}_{i}(u^{(a)}, u^{(b)}, v^{(abc)}) ~~\text{on}~~ \Gamma^{(abc)} \\ D^{(abc)}_{i} (\nabla_S v^{(abc)}_i \cdot n) &= 0 ~~\text{on}~~ \partial\Gamma^{(abc)}\end{split}\]