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Firstorder entropies for the DerridaLebowitzSpeerSpohn equation
Modeling the indirect contamination of a structured population with continuous levels of exposure
1.  Department of Mathematics, Texas A&M University, College Station, TX 778433368, United States 
Mathematically, the problem consists of an advectionreaction partial differential equation with variable speed, coupled by mean of its boundary condition to an ordinary differential equation. Using a method of characteristics, we prove the global existence, uniqueness and nonnegativity of the mild solution to this system, and also the global boundedness of the total population when subjected to controlled growth dynamics such as socalled logistic behaviors.
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