= Initial-boundary value problem
= IBVP
{c}
{synonym}
An initial-boundary value problem specifies a <partial differential equation>, <initial conditions>, and <boundary conditions>. For example, the half-line <wave equation> $u_{tt}=c^2u_{xx}$ requires an initial displacement and initial <velocity> for $x\geq0$ together with an endpoint condition such as $u(0,t)=0$ for $t>0$. Its meaning also depends on the chosen solution class: a <classical solution> satisfies the equation pointwise, while a <weak solution> satisfies an integrated form. These data must obey the compatibility conditions needed by the chosen regularity.
Back to article page
