Partial differential equations¶
Evans, L. C. (2010). Partial differential equations. American Mathematical Society.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Domain-specific¶
- Boundary Value Problem
- Well-posedness — existence of a solution, uniqueness, and continuous dependence on boundary data — depends on the equation type (elliptic, parabolic, hyperbolic), the domain geometry, and the combination of condition types; the elliptic Dirichlet problem (Laplace's or Poisson's equation on a bounded region with continuous boundary data) is the textbook well-posed prototype
This sourceEvans's textbook, which defines a well-posed problem as one having a solution, a unique solution, and continuous dependence on the data, with Hadamard's ill-posed Cauchy problem for Laplace's equation as the standard counterexample.
Supported in partVerified against a saved copy of the source
“problem for a partial differential equation is {{{well-posed}}} if (a) the problem in fact has a solution; (b)”
- Well-posedness — existence of a solution, uniqueness, and continuous dependence on boundary data — depends on the equation type (elliptic, parabolic, hyperbolic), the domain geometry, and the combination of condition types; the elliptic Dirichlet problem (Laplace's or Poisson's equation on a bounded region with continuous boundary data) is the textbook well-posed prototype
- Elliptic operator
Verification¶
Does it exist? Not checked yet. This entry carries no identifier to resolve. It was extracted from the citation as written in the article, normalized, and deduplicated against the rest of the registry.
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Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
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Registry ID ref:e2eb159c6bf5 · see in the full table