Lectures on Cauchy’s problem in linear partial differential equations
E334047
"Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Hadamard’s work on the Cauchy problem | 1 |
| Lectures on Cauchy’s problem in linear partial differential equations canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3167274 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lectures on Cauchy’s problem in linear partial differential equations Context triple: [Jacques Hadamard, notableWork, Lectures on Cauchy’s problem in linear partial differential equations]
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A.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
-
B.
Méthodes de calcul différentiel absolu et leurs applications
Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
-
C.
Cauchy–Kovalevskaya theorem
The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
-
D.
Singular Integrals and Differentiability Properties of Functions
"Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
-
E.
"Partial Differential Equations"
"Partial Differential Equations" is a foundational mathematical text that systematically develops the theory and methods for analyzing equations involving multivariable functions and their partial derivatives.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Lectures on Cauchy’s problem in linear partial differential equations Target entity description: "Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
-
A.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
-
B.
Méthodes de calcul différentiel absolu et leurs applications
Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
-
C.
Cauchy–Kovalevskaya theorem
The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
-
D.
Singular Integrals and Differentiability Properties of Functions
"Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
-
E.
"Partial Differential Equations"
"Partial Differential Equations" is a foundational mathematical text that systematically develops the theory and methods for analyzing equations involving multivariable functions and their partial derivatives.
- F. None of above. chosen
Statements (34)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| aim |
to clarify when the Cauchy problem is well-posed
ⓘ
to provide rigorous foundations for the Cauchy problem in linear PDEs ⓘ |
| associatedConcept |
Hadamard’s example of ill-posed problems
ⓘ
surface form:
Hadamard well-posedness
Hadamard’s definition of well-posed problems ⓘ |
| associatedWith | Jacques Hadamard’s work on ill-posed problems ⓘ |
| author | Jacques Hadamard ⓘ |
| authorNationality | French ⓘ |
| canonicalStatus | standard reference on the Cauchy problem for linear PDEs ⓘ |
| contribution | systematic development of the theory of the Cauchy problem for linear PDEs ⓘ |
| field |
mathematical analysis
ⓘ
partial differential equations ⓘ |
| focusesOn |
existence of solutions
ⓘ
uniqueness of solutions ⓘ well-posedness of problems ⓘ |
| hasInfluenced |
mathematical concept of well-posed problems
ⓘ
modern theory of partial differential equations ⓘ theory of hyperbolic equations ⓘ |
| historicalSignificance | classic treatise in the theory of linear PDEs ⓘ |
| language | French ⓘ |
| mainSubject |
Cauchy problem
ⓘ
linear partial differential equations ⓘ |
| mathematicalDiscipline | analysis of PDEs ⓘ |
| relatedTo |
Cauchy–Kovalevskaya theorem
ⓘ
surface form:
Cauchy–Kowalevski theorem
elliptic partial differential equations ⓘ hyperbolic partial differential equations ⓘ parabolic partial differential equations ⓘ |
| timePeriod | early 20th century mathematics ⓘ |
| topic |
conditions for existence of solutions
ⓘ
conditions for uniqueness of solutions ⓘ continuous dependence on initial data ⓘ initial value problems for PDEs ⓘ |
| usedIn | graduate-level studies in partial differential equations ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Lectures on Cauchy’s problem in linear partial differential equations Description of subject: "Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
Jacques Hadamard
→
notableWork
→
Lectures on Cauchy’s problem in linear partial differential equations
ⓘ
Hadamard’s example of ill-posed problems
→
appearsIn
→
Lectures on Cauchy’s problem in linear partial differential equations
ⓘ
this entity surface form:
Hadamard’s work on the Cauchy problem