Continuation of APPM 5470. Advanced study of the properties and solutions of elliptic, parabolic, and hyperbolic partial differential equations. Topics include the study of Sobolev spaces and ...

In this connection the subject of singular solutions of ordinary differential equations, and the conception of the characteristic in partial differential equations may be particularly mentioned.” ...

A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures. Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations For ...

Abstract. We devise algorithms for the numerical approximation of partial differential equations involving a nonlinear, pointwise holonomic constraint. The elliptic, parabolic, and hyperbolic model ...

Shih-Tong Tu, 杜詩統, Wen-Chieh Luo, 羅光杰, Erh-Tsung Chin, 秦爾聰, SOLUTIONS OF A CLASS OF N-TH ORDER ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS VIA FRACTIONAL CALCULUS, Taiwanese Journal of Mathematics, ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve.

Partial differential equations (PDEs) lie at the heart of many different fields of Mathematics and Physics: Complex Analysis, Minimal Surfaces, Kähler and Einstein Geometry, Geometric Flows, ...