Equações Diferenciais com Derivadas Parciais

Cod: 23057

Department: DCET

Department: DCET

ECTS: 10

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 260

Total contact time:

Total contact time:

Partial differential equations, Mathematical Analysis

Knowledge of the following topics is to be acquired by the students upon completion of this learning unit: (1) basic results and techniques on classical linear PDEs of Mathematical-Physics (heat, transport, waves, and Laplace), as well as (2) several representation techniques for solutions, and (3) some Functional Analysis methods for the study of linear PDEs.

After successfully completion of this learning unit the student must be able to mobilize his knowledge to study equations arising in modelling problems. Together with the abilities to be developed in the learning units Nonlinear

Analysis, Mathematical Modelling I, Mathematical Modelling II, Numerical

Methods for Partial Differential Equations, and Inverse Problems and Medical Imaging, this learning unit will contribute to a solid preparation of the students to tackle modelling issues involving partial differential equations.

1. Introduction: Mathematical modelling and partial differential equations

2. Classical linear equations of Mathematical Physics: heat, transport, waves, and Laplace

3. Nonlinear first order equations: method of characteristics, weak solutions,conservation laws

4. Several ways of representing solutions

5. Sobolev spaces

6. Second order linear elliptic equations

7. Linear evolution equations

1. Evans, L.C.: Partial Differential Equations, 2nd Ed., Graduate Studies in Mathematics, vol. 19, Providence: American Mathematical Society, 2010.

2. DiBenedetto, E.: Partial Differential Equations, Boston: Birkhauser, 1995.

3. Salsa, S. et al: A Primer on PDEs: Models, Methods, Simulations, (UNITEXT) vol. 65, Milan: Springer, 2013.

4. John, F.: Partial Differential Equations, 4th Ed., Applied Mathematical Sciences, vol. 1, New York: Springer-Verlag, 1982.

5. Garabedian, P.: Partial Differential Equations, AMS Chelsea vol. 325, Providence: American Mathematical Society, 1964.

6. Rafael Iório Júnior e Valéria de Magalhães Iório, Equações Diferenciais Parciais: uma Introdução, Projeto Euclides, IMPA, 2018.

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