Overdetermined problems in the context of elliptic partial differential equations concern boundary‐value formulations in which more conditions are prescribed than are generally required for a unique ...

Nonlinear eigenvalue problems arise when one seeks pairs (λ,u) satisfying an equation of the form F(λ,u)=0 in a function space, subject to boundary or decay conditions. In contrast to linear spectral ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

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: ...

Penn Engineers have developed a new way to use AI to solve inverse partial differential equations (PDEs), a particularly challenging class of mathematical problems with broad implications for ...