We consider a class of probability measure dependent dynamical systems which arise in the study of multiscale phenomena in diverse fields such as immunological population dynamics, viscoelasticity of polymers and rubber, and polarization in dielectric materials. We develop an inverse problem framework for studying systems with distributed temporal delays. In particular, we establish conditions for existence and uniqueness of the forward problem and well-posedness (including method stability under numerical approximations) for the inverse problem of estimating the probability measures. We show that a motivating class of models of HIV infection dynamics satisfies all the conditions of our framework, thereby providing a theoretical foundation for inverse problem computations with these models.
Contents
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Requires Authentication UnlicensedInverse problems for a class of measure dependent dynamical systemsLicensed
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Requires Authentication UnlicensedAnalytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problemsLicensed
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Requires Authentication UnlicensedGlobal uniqueness for a 3D/2D inverse conductivity problem via the modified method of Carleman estimatesLicensed
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Requires Authentication UnlicensedOn the use of fixed point iterations for the regularization of nonlinear ill-posed problemsLicensed