Cauchy boundary condition

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a Cauchy (French: [koʃi]) <a href="/facts/Boundary_value_problem/QEfmUqmP">boundary condition</a> augments an <a href="/facts/Ordinary_differential_equation/ygKGQ8kD">ordinary differential equation</a> or a <a href="/facts/Partial_differential_equation/DyPsBlv7">partial differential equation</a> with conditions that the solution must satisfy on the boundary; ideally so as to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and <a href="/facts/Normal_derivative/Fjc3JSVn">normal derivative</a> on the <a href="/facts/Boundary_(topology)/WgdH18kp">boundary</a> of the <a href="/facts/Domain_(mathematical_analysis)/xT44oI3E">domain</a>. This corresponds to imposing both a <a href="/facts/Dirichlet_boundary_condition/m9wsgG89">Dirichlet</a> and a <a href="/facts/Neumann_boundary_condition/0e0YBW4G">Neumann boundary condition</a>. It is named after the prolific 19th-century French mathematical analyst <a href="/facts/Augustin-Louis_Cauchy/aoTjgj6j">Augustin-Louis Cauchy</a>.
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Cauchy boundary condition open-in-new

Cauchy boundary condition