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- Weak_solution abstract "In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense. There are many different definitions of weak solution, appropriate for different classes of equations. One of the most important is based on the notion of distributions.Avoiding the language of distributions, one starts with a differential equation and rewrites it in such a way that no derivatives of the solution of the equation show up (the new form is called the weak formulation, and the solutions to it are called weak solutions). Somewhat surprisingly, a differential equation may have solutions which are not differentiable; and the weak formulation allows one to find such solutions.Weak solutions are important because a great many differential equations encountered in modelling real world phenomena do not admit sufficiently smooth solutions and then the only way of solving such equations is using the weak formulation. Even in situations where an equation does have differentiable solutions, it is often convenient to first prove the existence of weak solutions and only later show that those solutions are in fact smooth enough.".
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- Weak_solution wikiPageOutDegree "29".
- Weak_solution wikiPageRevisionID "607163469".
- Weak_solution wikiPageWikiLink Adjoint_of_an_operator.
- Weak_solution wikiPageWikiLink Category:Differential_equations.
- Weak_solution wikiPageWikiLink Category:Generalized_functions.
- Weak_solution wikiPageWikiLink Compact_support.
- Weak_solution wikiPageWikiLink Continuously_differentiable.
- Weak_solution wikiPageWikiLink Differentiable.
- Weak_solution wikiPageWikiLink Differentiable_function.
- Weak_solution wikiPageWikiLink Differential_operator.
- Weak_solution wikiPageWikiLink Distribution_(mathematics).
- Weak_solution wikiPageWikiLink Entropy_condition.
- Weak_solution wikiPageWikiLink Euclidean_space.
- Weak_solution wikiPageWikiLink Formal_adjoint.
- Weak_solution wikiPageWikiLink Fubinis_theorem.
- Weak_solution wikiPageWikiLink Function_(mathematics).
- Weak_solution wikiPageWikiLink Hamilton-Jacobi_equation.
- Weak_solution wikiPageWikiLink Hamilton–Jacobi_equation.
- Weak_solution wikiPageWikiLink Hermitian_adjoint.
- Weak_solution wikiPageWikiLink Hyperbolic_partial_differential_equation.
- Weak_solution wikiPageWikiLink Hyperbolic_system.
- Weak_solution wikiPageWikiLink Integration_by_parts.
- Weak_solution wikiPageWikiLink Mathematics.
- Weak_solution wikiPageWikiLink Multi-index.
- Weak_solution wikiPageWikiLink Multi-index_notation.
- Weak_solution wikiPageWikiLink Open_set.
- Weak_solution wikiPageWikiLink Ordinary_differential_equation.
- Weak_solution wikiPageWikiLink Partial_derivative.
- Weak_solution wikiPageWikiLink Partial_differential_equation.
- Weak_solution wikiPageWikiLink Real_number.
- Weak_solution wikiPageWikiLink Smooth_function.
- Weak_solution wikiPageWikiLink Smoothness.
- Weak_solution wikiPageWikiLink Support_(mathematics).
- Weak_solution wikiPageWikiLink Test_function.
- Weak_solution wikiPageWikiLink Viscosity_solution.
- Weak_solution wikiPageWikiLink Wave_equation.
- Weak_solution wikiPageWikiLink Weak_formulation.
- Weak_solution wikiPageWikiLinkText "Weak solution".
- Weak_solution wikiPageWikiLinkText "distributional sense".
- Weak_solution wikiPageWikiLinkText "weak sense".
- Weak_solution wikiPageWikiLinkText "weak solution".
- Weak_solution wikiPageWikiLinkText "weak solutions of nonlinear differential equations".
- Weak_solution hasPhotoCollection Weak_solution.
- Weak_solution subject Category:Differential_equations.
- Weak_solution subject Category:Generalized_functions.
- Weak_solution hypernym Function.
- Weak_solution type Agent.
- Weak_solution type Person.
- Weak_solution type ProgrammingLanguage.
- Weak_solution type Type.
- Weak_solution type Function.
- Weak_solution type Type.
- Weak_solution type Person.
- Weak_solution type Agent.
- Weak_solution type NaturalPerson.
- Weak_solution type Thing.
- Weak_solution type Q215627.
- Weak_solution type Q5.
- Weak_solution type Person.
- Weak_solution comment "In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense. There are many different definitions of weak solution, appropriate for different classes of equations.".
- Weak_solution label "Weak solution".
- Weak_solution sameAs Solución_débil.
- Weak_solution sameAs 弱解.
- Weak_solution sameAs m.09l8bm.
- Weak_solution sameAs Q7977966.
- Weak_solution sameAs Q7977966.
- Weak_solution sameAs 弱解.
- Weak_solution wasDerivedFrom Weak_solution?oldid=607163469.
- Weak_solution isPrimaryTopicOf Weak_solution.