Answer:-
A parabolic equation, like the heat equation, typically requires one initial condition and one or two boundary conditions, depending on the problem. The initial condition specifies the state of the system at the starting time, while boundary conditions define the behavior at the spatial boundaries. For a one-dimensional heat equation, you generally need one initial condition and two boundary conditions (Dirichlet, Neumann, or mixed). In higher dimensions, boundary conditions are needed for each spatial variable. The exact number depends on the domain and physical constraints, ensuring a well-posed problem with a unique and stable solution.
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