Some mass of material is released at the point z = 0. At t> 0 the material density evolves according to the formula p=t-1/2 exp P(-₁1). 4kt 1. Sketch p and against z (direct axis a to the right) at some moment t> 0 (no accuracy is required, just show general trends). 2. Verify that p satisfies the diffusion equation 8²p əx² др Ət = k 3. Find the flux of material as a function of r and t and show that at x = 1 the material is tranferred to the right and at x = −1 the material is tranferred to the left.

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