The search for mathematical models and their analyses born together with mathematical studies as power tools for the investigations of nature as aid to the daily problems that life is offering us is crucial. The growth and progress of mathematical methods in the last decades make the study of mathematical models critical in the quick advancement of the natural, physical, engineering, earth, life, and social sciences.

In the present special issue we would like to bring together papers covering a wide range of scientific interests concerned with differential equations emanating from mathematical models of classical fields such as solids and fluid mechanics and biology to economics and finance. The mathematical techniques are not only devoted to the search for numerical and exact solutions of the underlying differential equations for general and special problems but also include new theoretical developments suitable for novel applications of solving real world problems. Potential topics include, but are not limited to:

• Equivalence transformations and classical and nonclassical symmetries
• Reduction techniques and solutions and linearization
• Conserved quantities in natural phenomena
• Wave propagation
• Population dynamics and biological phenomena
• Cancer models
• Models for air pollution and underground pollution
• Reaction diffusion equations
• Mathematical methods for extended thermodynamics
• Hyperbolic reaction diffusion equations
• Numerical techniques for special problems in modeling
• Ad hoc methods for solutions
• Analysis of models in economics and finance

Before submission authors should carefully read over the journal’s Author Guidelines, which are located at http://www.hindawi.com/journals/aaa/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/submit/journals/aaa/mmmn/ according to the following timetable: