673 Partial Differential Equations

• Transport Equation
• Conservation Of Mass
• Untitled
• Momentum Balance
• Heat Equation
• Heat Equation Boundary Conditons
• Special Solution It Heat Equation
• Laplaces Equation
• Gradient Flows
• Wave Equation
• Special Solution To Drumhead
• Hamilton Jacobi Equation
• Classifying PDE
• Laplace Equation
• Representation Of Radial Solutions To Laplace
• Representation Continued
• Remarks about Solution
• Untitled
• Mean Value Formulas
• Maximum Principle
• Consequences Of Maximum Principle
• Mollifiers
• Regularity Of Harmonic Functions
• Estimating Derrivatives
• Consequences Of Derivative Estimates
• Harnack Inequality
• Greens Function And Solution To Δu=f, u=g
• Properties Of Greens Functions
• Greens Function On Half Plane
• Greens Half Plane Continued
• Untitled
• Dirichlet Principle
• Heat Equation
• Fundamental Solution
• Initial Value Problem
• Non Homogeneous Problem
• Non Homogenous Proof
• Weak Maximum Principle
• Strong Maximum Principle
• Mean Value Property
• Maximum Principle For Unbounded Domains
• Regularity
• Regularly Continued
• Energy Method
• Energy Method Continued
• Untitled
• Wave Equation
• Wave Equation D'alembert
• Reflection Metbod
• Spherical Means
• More Spherical Means
• Kirchhoffs Formula
• Remarks About Waves In 3D
• Poisson's Formula (n = 2)
• Wave Equation N>3
• Motivation Of Nonhomogenous Wave Equation
• Nonhomogenous Wave Equation
• More Nonhomogenous Wave
• Energy Methods Of Wave Equation
• Propagation And Energy
• Method Of Characteristics Intro
• Characteristic Ode
• Linear Examples
• Quasi linear Example
• Fully Nonlinear Example
• General Characteristics: Flatten Boundary
• Boundary/ Non characteristic Data
• Local Solutions Of Characteristic ODE
• Local Existence
• Local Existence Continued Again
• Linear Examples
• Quasi linear Examples
• Scalar Conservation Laws
• Rankine-hugonoit Jump Condition
• Nonuniqueness
• Viscous Approximation
• More Viscous Approximation
• Viscous Approximation Of Shocks
• Entropy Solutions
• Entropy Uniquness
• Entropy Uniqueness Continued
• Entropy Functions
• Remarks On Entropy Functions
• KruKov Theorem
• Untitled