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 ...

Xicheng Zhang, STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS DRIVEN BY LÉVY PROCESSES AND QUASI-LINEAR PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS, The Annals of Applied Probability, Vol. 22, No. 6 ...

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 ...

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, ...

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, ...

The honor, like a Nobel Prize for mathematics, was given this year to Luis Caffarelli for his work on partial differential equations.