PARTIAL DIFFERENTIAL EQUATIONS

Prerequisites & course information

Requisites: Graduate/professional standing or declared in Mathematics VISP (graduate or dissertator) Course Designation: Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: No Last Taught: Spring 2026 Learning Outcomes: 1. Analyze notions of weak solutions to linear and nonlinear initial value problems defined by partial differential equations of first-order, elliptic, parabolic, and hyperbolic types. Audience: Graduate 2. Analyze proof methods to establish uniqueness and existence of weak solutions to partial differential equations. Audience: Graduate 3. Investigate regularity of weak solutions via various different viewpoints. Audience: Graduate 4. Illustrate the general theory by applying it to concrete examples. Audience: Graduate 5. Investigate parameter dependence of weak solutions to both linear and nonlinear PDE Audience: Graduate Learning Outcomes: 1. Analyze notions of weak solutions to linear and nonlinear initial value problems defined by partial differential equations of first-order, elliptic, parabolic, and hyperbolic types. Audience: Graduate 2. Analyze proof methods to establish uniqueness and existence of weak solutions to partial differential equations. Audience: Graduate 3. Investigate regularity of weak solutions via various different viewpoints. Audience: Graduate 4. Illustrate the general theory by applying it to concrete examples. Audience: Graduate 5. Investigate parameter dependence of weak solutions to both linear and nonlinear PDE Audience: Graduate