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Regularization of a non‐characteristic Cauchy problem for the heat equation
Author(s) -
Hào Dinh Nho
Publication year - 1992
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670150803
Subject(s) - mathematics , cauchy problem , heat equation , regularization (linguistics) , initial value problem , mathematical analysis , stability (learning theory) , mathematical physics , artificial intelligence , machine learning , computer science
The non‐characteristic Cauchy problem for the heat equation u xx ( x , t ) = u 1 ( x , t ), 0 ⩽ x ⩽ 1, − ∞ < t < ∞, u (0, t ) = φ( t ), u x (0, t ) = ψ( t ), − ∞ < t < ∞ is regularizèd when approximate expressions for φ and ψ are given. Properties of the exact solution are used to obtain an explicit stability estimate.