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- W617967151 abstract "Publisher SummaryThis chapter presents the applications to partial differential equations. The chapter makes the classification about the classical and the generalized solutions. However, there is one important difference. In the case of the ordinary differential equation Lu = 0 with constant coefficients, every solution is the classical solution. The matter is quite different for partial differential equations. The solutions in a similar situation may now include generalized functions. A function u(x) is called a classical solution of the partial differential equation. The theory of partial differential equations stems from the intensive and extensive study of a few basic equations of mathematical physics, and the coefficients in all of these are constants. Such equations arise in the study of gravitation, electromagnetism, perfect fluids, elasticity, heat transfer, and quantum mechanics. The chapter derives the formulas for the discontinuities across a surface element of the second-order partial derivatives of a harmonic function because of single- and double-layer potentials. The chapter also re derives and examines the fundamental solution of the Laplace operator." @default.
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- W617967151 date "1983-01-01" @default.
- W617967151 modified "2023-09-26" @default.
- W617967151 title "10 Applications to Partial Differential Equations" @default.
- W617967151 doi "https://doi.org/10.1016/s0076-5392(08)62520-5" @default.
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