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28 Março 2019, 11:00 • Hugo Tavares

Trabalho autónomo dos alunos.

Lecture 10: The Wave Equation, part II

26 Março 2019, 10:30 • Hugo Tavares

The wave equation in dimension 1: a stability result, cone of dependence, cone of influence.

The Nonhomogeneous equation: Duhamel's principle.The wave equation in dimension N>1: uniqueness results in a bounded domain and in the whole R^N by energy methods.

Lecture 9: The Heat Equation, part III. The Wave Equation, part I

22 Março 2019, 12:00 • Hugo Tavares

The homogeneous problem in the whole space: some remarks about admissible initial data.The nonhomogeneous problem: Duhamel's principle.

The Wave Equation: - deduction- initial and boundary conditions.- The D'Alembert formula and stability result (dimension 1)

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21 Março 2019, 11:00 • Hugo Tavares

Trabalho autónomo dos alunos.

Lecture 8: The Heat Equation, part II

19 Março 2019, 10:30 • Hugo Tavares

Proof of the uniqueness result for the initial/boundary value problem using energy methods.

The fundamental solution of the heat equation. Solution to the initial value problem in the whole space.