Fitting parameters of a Fokker-Planck-like equation with constraint

TL;DR

This paper investigates a Fokker-Planck-like equation with a scalar parameter to satisfy an integral constraint, establishing conditions for solution existence and uniqueness, motivated by tumor immune control applications.

Contribution

It introduces criteria for existence and uniqueness of solutions to a constrained Fokker-Planck-like equation, including counter-examples, with applications to tumor immune response modeling.

Findings

Criteria for solution existence and uniqueness

Counter-examples illustrating limitations

Application relevance to tumor immune control

Abstract

We analyse a Fokker-Planck like equation, driven by a scalar parameter in order to reach an integral constraint. We exhibit criteria guaranteeing existence-uniqueness of a solution. We also provide counter-examples. This problem is motivated by an application to the immune control of tumor growth.