Optimal pollution control with a nonconstant exponential rate of decay

This paper examines the effects of introducing a nonconstant exponential pollution decay rate into a pollution control model. If the pollution level is great enough it may render a waterway biologically dead and unable to cleanse itself. This is the problem associated with Lake Erie and Lake Baikal. The natural question is: Is it ever optimal to let a waterway such as Lake Erie die? The answer is shown to depend upon the form of the objective functional used by the planning authorities. The possibility of multiple stationary solutions also arises.