One service mathematics has rendered the 'Et moi, ... si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aIle.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non sense'. The series is divergent; thererore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a...

Modeling and Applied Mathematics Modeling the behavior of real physical systems by suitable evolution equa- tions is a relevant, maybe the fundamental, aspect of the interactions be- tween mathematics and applied sciences. Modeling is, however, only the first step toward the mathematical description and simulation of systems belonging to real world. Indeed, once the evolution equation is proposed, one has to deal with mathematical problems and develop suitable simula- tions to provide the description of the real system according to the model. Within this framework, one has an evolution...

This is a collection of four lectures on some mathematical aspects related to the nonlinear Boltzmann equation. The following topics are dealt with: derivation of kinetic equations, qualitative analysis of the initial value problem, singular perturbation analysis towards the hydrodynamic limit and computational methods towards the solution of problems in fluid dynamics.

This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions.

Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the...

This book has the aim of dealing with the Nonlinear evolution problems related to the spatially dependent Boltzmann and Enskog equations.

This volume illustrates approaches to analyzing problems in fracture mechanics. It examines the application of asymptotic analysis to strength evaluation in models of elastic structures and geophysics. In addition, it provides analytical techniques for studying singularly perturbed problems.