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- W200417975 abstract "This chapter discusses the equation of heat conduction. Upon denoting the sum of the second-order derivatives by 2u, one can write the equation of heat conduction in the form: 2δuδt+fx,y,z,t. The chapter explains the problem of heat conduction in an unbounded medium and solves Cauchy's problem for the above mentioned equation. Suppose that for t > 0, a certain function u is given that has continuous derivatives with respect to the space coordinates up to the second-order inclusive and a first-order derivative with respect to time. Suppose, also, that u and its first-order derivatives are bounded throughout space. The smoothness of its solution distinguishes the equation of heat conduction in an essential way from the equation for a vibrating string or from the wave equation" @default.
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- W200417975 date "1964-01-01" @default.
- W200417975 modified "2023-09-24" @default.
- W200417975 title "THE EQUATION OF HEAT CONDUCTION" @default.
- W200417975 doi "https://doi.org/10.1016/b978-0-08-010424-9.50014-7" @default.
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