JADEs Issue # 1: Intro & 3 PDEs to Explore

INTRODUCTION

Welcome to the inaugural issue of this new Open Access (OA) journal, The Journal of Applied Differential Equations (JADEs), covering both linear and nonlinear partial differential equations (PDEs) and ordinary differential equations (ODEs) and the analytic methods/solutions of these.

While most journals take a very theory-driven approach to PDEs and ODEs, this journal will discuss and illustrate problems from a very pragmatic, workshop problem-solution focus for applied/industrial mathematicians, scientists (physicists, chemists, etc.), engineers (mechanical, electrical, maybe some structural), and others.

Please subscribe if you want to see more problems like the one below as well as other more relevant PDEs and/or ODEs with applications in mechanics (analytical, classical, Newtonian), electromagnetic field/quantum-based wave mechanics, fluid mechanics and more.

With that said, here are some problems below for your consideration.

PROBLEM 1

The following nonlinear partial differential equation (PDE) can yield a multiplicative separable general solution with a function f for a > 0.

Definition

Reference: Polyanin et al, "Handbook of Nonlinear Partial Differential Equations, 2nd Edition," Chapman & Hall/CRC Press (Dec 2011).

Example

PROBLEM 2

The following problem is a first order PDE that yields a principle integral solution.

Definition

Reference: Polyanin et al, "Handbook of First Order Partial Differential Equations," Taylor & Francis (2002).

Example

PROBLEM 3

The following nonlinear PDE problem is excerpted from my recently published book.

Definition

Example

Reference: Anglin, "PDEs of Fluid Mechanics" (2022):

ABOUT THE EDITOR

Steve Anglin, M.Sc. Ph.D. (h.c.) is an applied, industrial mathematician solving partial differential equations (PDEs) with applications in the fields of fluid mechanics (mechanical engineering) as well as some electrical engineering and physics. He is a former lecturer of mathematics at Case and Saint Leo Universities. Steve received his Master of Science (M.Sc.) in applied mathematics from Brown University (Ivy League) and his Hon. Doctorate (Ph.D.(h.c.)) in mathematics from Trinity College. Previously, he published or has been credited on 2,000+ technical trade books with Springer Nature and Pearson Education as well as 2 eZines with O'Reilly Media.

For more, visit: https://www.amazon.com/author/steveanglin

Email: [email protected]