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Mathematics LibreTexts

4.5: Initial-Boundary Value Problems

In previous sections we looked at solutions defined for all \(x\in\mathbb{R}^n\) and \(t\in\mathbb{R}^1\). In this and in the following section we seek solutions \(u(x,t)\) defined in a bounded domain \(\Omega\subset\mathbb{R}^n\) and for all \(t\in\mathbb{R}^1\) and which satisfy additional boundary conditions on \(\partial\Omega\).

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