Related papers: On applications of conservation laws in pharmacoki…
A lot of criticism against the standard formulation of pharmacokinetics has been raised by several authors. It seems that the natural reaction for that criticism is to comment it from the point of view of the theory of conservation laws.…
In the text S.Piekarski, M.Rewekant,(arXiv:1208.3847)it has been mentioned that some information on bioavailability and bioequivalence of drugs can be obtained from simulations based on the conservation laws. Here we shortly discuss that…
Augmented variational principles are introduced in order to provide a definition of relative conservation laws. As it is physically reasonable, relative conservation laws define in turn relative conserved quantities which measure, for…
Some inconsistencies in the passive pharmacokinetics has been observed many years ago. It is possible these inconsistencies result from the lack of proper evolution equations. In this communication, this possibility is illustrated on the…
Conservation laws are the pillars of physics. It's what we held on to when our imagination was challenged during the days of relativity or quantum mechanics. Their violation leads to the most absurd models, so excellently exercised in the…
In studies of interfaces with dynamic chemical composition, bulk and interfacial quantities coupled via surface conservation laws of excess surface quantities. While this approach is for microscopically sharp interfaces, its applicability…
We present a novel method to improve pharmacokinetics modeling, an essential step of drug development. Conventional models frequently fail to fully represent the intricacies of drug absorption and distribution, which limits their predictive…
In a recent paper, PNAS, 118, e1921529118 (2021), it was argued that while the standard definition of conservation laws in quantum mechanics, which is of a statistical character, is perfectly valid, it misses essential features of nature…
We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics." The presence of…
Well known biological approximations are universal, i.e. invariant to transformations from one species to another. With no other experimental data, such invariance yields exact conservation (with respect to biological diversity and…
A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription…
In this work we consider companion conservation laws to general systems of conservation laws. We investigate sufficient regularity for weak solutions to satisfy companion laws, assuming the fluxes to be $C^{1,\gamma}$, $0<\gamma<1$,…
This note aims at providing a rather informal and hopefully accessible overview of the fairly long and technical work [4]. In that paper, the authors established new global-in-time existence results for admissible solutions of nonlinear…
We explore new ways of regulating defect behavior in systems of conservation laws. Contrary to usual regularization schemes (such as a vanishing viscosity limit), which attempt to control defects by making them smoother, our schemes result…
Fractional-order dynamical systems were recently introduced in the field of pharmacokinetics where they proved powerful tools for modeling the absorption, disposition, distribution and excretion of drugs which are liable to anomalous…
The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…
In this short note, we provide a partial extension of Rivi\`ere's convervation law in higher dimensions under certain Lorentz integrability condition for the connection matrix. As an application, we obtain a conservation law for weakly…
We investigate conservation laws of diffusion-convection equations to construct first-order potential systems corresponding to these equations. We do two iterations of the construction procedure, looking, in the second step, for the…
The laws expressing conservation of momentum and energy apply to any isolated system, but these laws are violated for for highly viscous liquids under laboratory conditions because of the unavoidable interactions with the measuring…
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…