Lectures related to Maximum Principle in Heat Equation

Heat Equation: Separation of Variables

Covers the application of separation of variables method to solve the heat equation.

Optimal Transport: In-Depth Evaluation

Explores optimal transport theory with a focus on heat equations and Wasserstein distance.

Fourier Analysis and PDEs

Explores Fourier analysis, PDEs, historical context, heat equation, Laplace equation, and periodic boundary conditions.

Diffusion Equation

Covers the Fourier law, heat equation, Righi-Leduc effect, and related experiments.

Heat Equation: Stationary Distribution

Explores the heat equation, equilibrium equations, heat flux, and harmonic functions in heat distribution.

Maximum Entropy Principle: Stochastic Differential Equations

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Heat Equation: Core and Solutions

Explores the heat equation core, solutions, and diffusion behavior over time.

Free Propagation and Heat Equation

Covers free propagation and the heat equation solution, discussing momentum preservation and Fourier multipliers.

Convolution and Fourier Transform

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

Thermo-mechanics: Thermal and Mechanical Problems

Explores thermal and mechanical problems in thermo-mechanics, covering the heat equation, total strain, and stress analysis modeling.

Thermal Diffusion: Basics and Applications

Explores thermal diffusion, specific heat, conductivity, and expansion in materials, explaining how energy is transferred between atoms and molecules.

Optimal Transport: Gradient Flows

Explores optimal transport, gradient flows, the implicit Euler scheme, and the heat equation in the context of Dirichlet energy functional.

Heat Equation in 1D: Chapter 12

Explores the heat equation in 1D, emphasizing conservation of thermal energy and numerical solution methods.

Heat Equation: Diffusion

Covers the heat equation for diffusion and conservation of thermal energy.

Function Approximations

Covers continuous functions with compact support, density, and approximation, focusing on the heat equation.

Heat Equation: Fourier Series

Explores the heat equation solutions using Fourier series and energy conservation.

Laplacian: Basics and Examples

Covers the basics of the Laplacian operator applied to scalar fields and its importance in mathematical models.

Equations of Heat and Fourier Transform

Covers heat equations, Fourier transforms, and variable separation methods.

Finite Element Discretization: Heat Equation

Explores finite element discretization of the heat equation and its verification process.