Boundary value problems for nonlinear partial differential equations form a cornerstone of modern mathematical analysis, bridging theoretical advancements and practical real-world applications. These ...

Recent decades have witnessed a bloom in research at the interface of complex geometry and nonlinear partial differential equations. This interdisciplinary field explores the deep and intricate ...

In this paper closed-form solutions for the evaluation of the stress-field in a rigid perfectly-plastic body under plane-stress or plane-strain conditions are estimated. The two nonlinear partial ...

We consider a specific type of nonlinear partial differential equation (PDE) that appears in mathematical finance as the result of solving some optimization problems. We review some examples of such ...

An advanced course in the analytical and numerical study of ordinary and partial differential equations, building on techniques developed in Differential Equations I. Ordinary differential equations: ...

Two difference-approximation schemes to a nonlinear pseudo-parabolic equation are developed. Each of these schemes is stable and possesses a unique solution which can be obtained by an iterative ...

Office: Korman Center 290 dma68@drexel.edu Phone: 215.895.6247 David M. Ambrose works in mathematical analysis and scientific computing for nonlinear systems of partial differential equations arising ...

Nonlinear waves; integrable systems; solitons; mathematical modeling in social and behavioral science. The study of wave phenomena by means of mathematical models often leads to a certain class of ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...