**What is reaction-diffusion system ?:**

Reaction-diffusion systems are one of partial differential equations. They are often used as mathematical models which correspond to several physical phenomena, such as the spatio-temporal distribution of chemical substances which are transformed into each other by chemical reactions and diffuse randomly. This system can also describe dynamical phenomena not only in cgemistry but also in biology, geology and physics. For m-componet chemical substances, the system is represented by

where the diffusion coeficients d_j are non-negative and the nonlinear term f_j are smooth functions..

**Patterns:**

Diffusion is the movement of particles from the high density region to the low density region. Thus it makes the distribution homogenize. We can see that the ink is desolved into water. However, this observation is not true if the number of chemical substances are increased. In this situation many patterns are obserevd in the following figures: crystal groth and the animal coat pattern.

**Diffusion-induced phenomena**- Diffusion-induced instability
- Diffusion-induced extinction
- Diffusion-induced blowup
- Diffusion-preventing blowup

**Propagation phenomena****Attractors, Entire solutions****Reaction-diffusion approximation**- Stefan problem
- Cross-diffusion system, nonlinear diffusion
- Non-local kernel
- Wave equation

**Reserach by students**

Motion of planets ann collisions

Fields of Research