Partial Differential Equations
Objectives
To provide the students with the right set of tools to follow a thesis on the topic.
General characterization
Code
11590
Credits
6.0
Responsible teacher
Fábio Augusto da Costa Carvalho Chalub
Hours
Weekly - 4
Total - 62
Teaching language
Português
Prerequisites
BSc in Math of similar subjects.
Bibliography
EDP um curso de Graduação, Valéria Iório, Coleção Matemática Unviersitária (basic) e Introduction to Partial Differntial Equations, Gerald Folland, Princeton (advanced).
Teaching method
Tutorial classes.
Evaluation method
Homework and seminars.
Subject matter
1. Preliminaries: notation, convolution, distributions. Approximations of identity, Dirac delta.
2. Partial Differential Equations (classic): heat equation, wave equation, Laplace equation in bounded and unbounded domains. Existence, uniqueness, solution by series, and Fourier transform. Fundamental solutions. Maximum principle. Characteristics.
3. Sobolov spaces, weak differentiation, density arguments.
4. Extra topics: pseudo-differential operators, integro-differential operators, applications.