Question

Consider the mass density , u(x,t), in the region [0,2]. where source is R(x) =x−1. The...

Consider the mass density , u(x,t), in the region [0,2]. where source is R(x) =x−1. The flux rule is φ(x) = (u−1)2 and the initial condition is u(x,0) =x.

(1) what is the continuity equation and at what point is density not changing ,ut= 0.

(2) is the total mass (U=∫udx) changing?

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Homework Answers

Answer #1

1) The flux is given to be

The flux is the change in mass density.

So,

For the mass density to not change, du/dt = 0

So, for u in the range 0 to 2,

The point where mass density doesn't change is

u = 1

2) the mass density at a time t is given by integrating the equation.

The total change in mass is given by

so, the total mass is changing.

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