This book gathers selected works covering research in mathematics on new methods and techniques for the applications of differential equations, presented at the 12th International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES), held in Saints Constantine and Helena, Bulgaria, from September 14, 2025.
The book is organized around eight key themes, with applications in mathematical physics, mathematical biology, financial mathematics, mechanics, fractional analysis, numerical methods, big data and computer science, and artificial intelligence and neural networks.
By showcasing fundamental research in both theoretical and applied mathematics, this book aims to promote new tools and approaches that can effectively address real-life challenges through the application of differential equations.
Weighted resolvent estimates for Laplace Operator with point
interactions.- Cauchy Problem for Non-local Parabolic PDEs.- From Lipschitz
to One Sided Lipschitz.- Short Overview of the Advances in the SEsM
Methodology for Obtaining Exact Solutions of Nonlinear Differential
Equations.- Simulations of Local Characteristics on Flow, Heat Transfer, and
Electrostatics, Using Potentials by Analytical Functions.- Exact Solutions of
a Model Equation for Shallow-Water Waves.- Localized Traveling Waves in a
Spatio-Temporal Population Interaction Model.- Investigation of Fire Wave
Dynamics in Forest Ecosystems via a Hyperbolic Advection - Reaction-Diffusion
Equation: Part I. Analytical Solutions.- Travelling Wave Solutions for a
Two-Species Competitive Model in Ecology.- Explicit Formulae to the Solutions
of the Cauchy Problem for Schrödinger Type Linear PDEs Depending on Small
Parameter.- Application of Ordinary Differential Equations for Modeling the
Cutting Process in Robotic Harvesting of Fruits and Vegetables.- Exact
solutions of another model equation for shallow-water waves.
Angela Slavova graduated from the University of Ruse, Bulgaria, with a degree in computer engineering and obtained her master's degree in 1986. From 1992 to 1993, she was awarded Fulbright Scholarship at the Florida Institute of Technology, Florida, USA. She earned her Ph.D. in mathematics in 1994. Since 2004, Professor Slavova has served as Head of the Department of Mathematical Physics at the Institute of Mathematics, Bulgarian Academy of Sciences. Since 2023, she has held the position of Full Professor at the Institute of Mechanics, Bulgarian Academy of Sciences.
