Consider the PDE $$\partial_t u + au + b\partial_x u + c\partial^2_{xx} u + d\partial^3_{xxx} u + e\partial^4_{xxxx} u + f\partial^5_{xxxxx} u + \dots= 0.$$ in $(0,\infty) \times \mathbb{R}$, with $a,b,c,d,f \in \mathbb{R}$.

I've seen multiple times people referring to certain terms in such equations as transport term, diffusion term, dispersion term, dissipation term, viscosity term, and so on.

I can see why one would call $c\partial^2_{xx}u$ a viscosity term (from the vanishing viscosity technique), but I don't know which terms of the equation the other names apply to and why. Can you offer some explanation?

Consider the PDE $$\partial_t u + au + b\partial_x u + c\partial^2_{xx} u + d\partial^3_{xxx} u + e\partial^4_{xxxx} u + f\partial^5_{xxxxx} u + \dots= 0.$$ in $(0,\infty) \times \mathbb{R}$, with $a,b,c,d,f, \dots \in \mathbb{R}$.

I've seen multiple times people referring to certain terms in such equations as transport term, diffusion term, dispersion term, dissipation term, viscosity term, and so on.

I can see why one would call $c\partial^2_{xx}u$ a viscosity term (from the vanishing viscosity technique), but I don't know which terms of the equation the other names apply to and why. Can you offer some explanation?

Consider the PDE $$\partial_t u + au + b\partial_x u + c\partial^2_{xx} u + d\partial^3_{xxx} u + e\partial^4_{xxxx} u + f\partial^5_{xxxxx} u + \dots= 0.$$ in $(0,\infty) \times \mathbb{R}$, with $a,b,c,d,f \in \mathbb{R}$.

I've seen multiple times people referring to certain terms in such equations as diffusion term, dispersion term, dissipation term, viscosity term, and so on.

I can see why one would call $c\partial^2_{xx}u$ a viscosity term (from the vanishing viscosity technique), but I don't know which terms of the equation the other names apply to and why. Can you offer some explanation?

Consider the PDE $$\partial_t u + au + b\partial_x u + c\partial^2_{xx} u + d\partial^3_{xxx} u + e\partial^4_{xxxx} u + f\partial^5_{xxxxx} u + \dots= 0.$$ in $(0,\infty) \times \mathbb{R}$, with $a,b,c,d,f \in \mathbb{R}$.

I've seen multiple times people referring to certain terms in such equations as transport term, diffusion term, dispersion term, dissipation term, viscosity term, and so on.

I can see why one would call $c\partial^2_{xx}u$ a viscosity term (from the vanishing viscosity technique), but I don't know which terms of the equation the other names apply to and why. Can you offer some explanation?