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# 4.5: Initial-Boundary Value Problems

• Page ID
2152
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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 $$\partial\Omega$$.

### Contributors

• Integrated by Justin Marshall.