\fA1.4 2nd order BOD decay. A modied Streeter-Phelps model is obtained if the as- sumption of proportional BOD decay is replaced by the assumption of 2nd order BOD decay. One has then 6b 6b _ 2 6 ('9 (4.2) EC + vi = k1b2 + k2(cs c), where parameters In, kg, (:5, v are positive constants (see also the example at the end of SectiOn 1.2.2 in class). a) What are the physical dimensions of the parameter k1? Compare this against [91 in the original Streeter-Phelps model (2.1)-(2.2). b) Transform (4.1)-(42.2) into the moving frame coordinate system and study the resulting equations in the phase plane. How do they behave as as t > 00? Do they display an oasygen-sag? Does the model preserves positivity, i.e. will the solution remain non-negative for positive initial data