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First-order entropies for the Derrida-Lebowitz-Speer-Spohn 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 77843-3368, United States |
Mathematically, the problem consists of an advection-reaction 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 so-called logistic behaviors.
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