This book presents new developments in non-local mathematical modeling and mathematical
analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in
mechanics thermo-dynamics game theory and theoretical biology are examined in details. It
starts off with a review and summary of the basic ideas of mathematical modeling frequently
used in the sciences and engineering. The authors then employ a number of models in bio-science
and material science to demonstrate applications and provide recent advanced studies both on
deterministic non-local partial differential equations and on some of their stochastic
counterparts used in engineering. Mathematical models applied in engineering chemistry and
biology are subject to conservation laws. For instance decrease or increase in thermodynamic
quantities and non-local partial differential equations associated with the conserved physical
quantities as parameters. These present novel mathematical objectsare engaged with rich
mathematical structures in accordance with the interactions between species or individuals
self-organization pattern formation hysteresis. These models are based on various laws of
physics such as mechanics of continuum electro-magnetic theory and thermodynamics. This is
why many areas of mathematics calculus of variation dynamical systems integrable systems
blow-up analysis and energy methods are indispensable in understanding and analyzing these
phenomena. This book aims for researchers and upper grade students in mathematics engineering
physics economics and biology.
