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- W2083230708 abstract "Let u(x, t) satisfy the heat equation in 0<x<1, 0<t≤T. Let u(x, 0)=0 for 0<x<1 and let |u(0, t)|<ε, | ux(0, t) |<ε, and | u(1, t) |<M for 0≤t≤T. Then, $$left| {uleft( {x, t} right)} right|< M_{1^{1 - beta left( x right)varepsilon beta left( x right)} } $$ , where M1 and β(x) are given explicitly by simple formulas. The application of the a priori bound to obtain error estimates for a numerical solution of the Cauchy problem for the heat equation with u(x, 0)=h(x), u(0, t)=f(t), and ux(0, t)=g(t) is discussed." @default.
- W2083230708 created "2016-06-24" @default.
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- W2083230708 date "1964-12-01" @default.
- W2083230708 modified "2023-10-16" @default.
- W2083230708 title "A Cauchy problem for the heat equation" @default.
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- W2083230708 doi "https://doi.org/10.1007/bf02412441" @default.
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