Xinwei Yu

Area of Study / Keywords

Partial Differential Equations; Fluid Mechanics; Wireless Communications

MATH 436 - Intermediate Partial Differential Equations

Partial differential equations as physical models. Introduction to basic generalized functions. Theory of linear and quasi-linear first-order equations: general solution, initial value problem, generalized solutions and propagation of singularities, characteristic surfaces, shock formation. Theory of fully nonlinear first order equations: complete solution and the initial value problem. Hamilton-Jacobi equation and its applications. Second order linear equations in n dimensions: classification, canonical form, characteristic surfaces and shock formation, initial and boundary value problem. Prerequisite: MATH 300 or MATH 337.

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