Structured populations, cell growth and measure valued balance laws

Structured Populations, Cell Growth and Measure Valued Balance Laws

A well-posedness theory of measure valued solutions to balance laws is presented. Nonlinear semigroups are constructed by means of the operator splitting algorithm. This approach allows to separate the differential terms from the integral ones, leading to a significant simplification of the proofs. Continuous dependence with respect to parameters is also shown. The whole framework allows a unif...

Balance laws in Continuum Mechanics: a measure-theoretical approach

The author wishes to express special thanks to Marco Degiovanni for his deep and incessant teaching and to Alfredo Marzocchi for his help and kindness. A Elena, mia moglie e fonte del mio entusiasmo Contents Introduction v 1 Review of measure theory and Cauchy interactions 1 1. Bibliography 83 iv Introduction B alance laws are a basic concept in Continuum Mechanics and apply to many situations,...

Balance Laws

Central to any theory of continuum mechanics, are balance laws of mass, momentum, and energy. These provide us with universal relations, which should be satisfied during every process associated with the continuous body. However, to obtain general statements of these laws, several integral theorems are required. A major portion of this chapter therefore deals with divergence theorem, Stokes’ th...

The mutation-drift balance in spatially structured populations.

In finite populations the action of neutral mutations is balanced by genetic drift, leading to a stationary distribution of alleles that displays a transition between two different behaviors. For small mutation rates most individuals will carry the same allele at equilibrium, whereas for high mutation rates of the alleles will be randomly distributed with frequencies close to one half for a bia...

Causal Laws and Multi - Valued