Initial and boundary conditions are two important types of supplementary conditions in partial differential equations. They help us describe a particular problem, not only a general equation. In a partial differential equation, the unknown function usually depends on more than one independent variable. For example, in a heat problem, the unknown function may depend on position $x$ and time $t$. The equation gives the law or rule. But the equation alone does not usually describe one particular physical situation. We must also give suitable conditions.

Initial and boundary conditions are two important types of supplementary conditions in partial differential equations. They help us describe a particular problem, not only a general equation. In a partial differential equation, the unknown function usually depends on more than one independent variable. For example, in a heat problem, the unknown function may depend on position $x$ and time $t$. The equation gives the law or rule. But the equation alone does not usually describe one particular physical situation. We must also give suitable conditions.