Lectures on Cauchy's Problem in Linear Partial Differential Equations¶
Hadamard, J. (1923). Lectures on Cauchy's Problem in Linear Partial Differential Equations. Yale University Press.
Cited by¶
1 citation across 1 artifact.
Each citation links to the sentence it supports in the citing article.
Domain-specific¶
- Differential equation
- The theory of existence, uniqueness, and continuous dependence on data — well-posedness, in Hadamard's formulation — determines when the equation actually has a unique solution that varies stably with the input data, and its absence signals physical or mathematical ill-posedness rather than modelling failure
This sourceHadamard's own definition of a correctly set boundary problem as one whose accessory conditions determine one and only one solution, together with his demonstration that Cauchy's problem for the equation of potentials does not depend continuously on its data.
Supported in partVerified against a saved copy of the source
“if those accessory conditions are such as to determine one and only one solution of the indefinite equation”
- The theory of existence, uniqueness, and continuous dependence on data — well-posedness, in Hadamard's formulation — determines when the equation actually has a unique solution that varies stably with the input data, and its absence signals physical or mathematical ill-posedness rather than modelling failure
Verification¶
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