Explain the following concepts. Give an example in each case. - Initial Condition - Boundary conditions...

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Explain the following concepts. Give an example in each case. - Initial Condition - Boundary conditions - - - - - - - Initial-value problem Boundary-value problem Initial-boundary-value problem Well-posed problem Differential operator Linear differential operator Linear homogeneous PDE Linear nonhomogeneous PDE - Principle of superposition Dirichlet boundary condition Neumann condition - - - Robin condition Hyperbolic second-order PDE Parabolic second-order PDE - Elliptic second-order PDE Explain the following concepts. Give an example in each case. - Initial Condition - Boundary conditions - - - - - - - Initial-value problem Boundary-value problem Initial-boundary-value problem Well-posed problem Differential operator Linear differential operator Linear homogeneous PDE Linear nonhomogeneous PDE - Principle of superposition Dirichlet boundary condition Neumann condition - - - Robin condition Hyperbolic second-order PDE Parabolic second-order PDE - Elliptic second-order PDE