In the presence that most books are either too mathematical or too physical, this book is written with the belief that mathematical methods should be communicated to a wider audience than just mathematicians. It offers new physical models and new mathematical approaches that are disperse throughout the research journals in the last years. The physical objective is to model thermoelectric and thermoelectrochemical phenomena. The mathematical aim is to establish existence results in a simple setting from existence theory on PDE for providing quantitative estimates, and in such way their application may be useful for the understanding of the data dependence. This book tries to open one bridge between the PDE researchers and scientists and engineers in the natural and technological fields. Although this volume has some rather theoretical aspects of mathematical structure, it outlines a tool and new approaches for using in both research and postgraduate levels. This book is targeted at all researchers concerned with modeling, the conceptual basis of mathematical methods and how the PDE theory may be applied for their fields of research.

Luisa Consiglieri, independent researcher. B.S., M.S., Ph.D. in mathematics from Lisbon Univ. in 1988, 1992, 2000, respectively. Teaching positions at Sci. Fac. of Lisbon Univ., 1987-2009. Tenured position (Assistant Prof.) until her retirement. Her research interests span a variety of areas in differential equations and their real-world modeling.