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Partial Differential Equations

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Partial Differential Equations

(偏微分方程)

Reference Books:

Lawrence C. Evans, Partial differential equations, Providence, R.I. : American Mathematical Society, 1998

Fritz John, Partial differential equations, 4th Edition, New York : Springer-Verlag, 1982

Contents include the following:

1. first-order equation, conservation laws 2. Cauchy-Kovalevskaya theorem

3. Laplace’s equation, 4. heat equation 5. wave equation 6. Fourier transform

7. Sobolev spaces, Sobolev inequalities, compact embedding

8. second-order elliptic equation, weak solution, Lax-Milgram theorem, Fredholm alternative, maximum principle, regularity

9. second-order parabolic equation, Galerkin method, maximum principle

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