Unformatted text preview: v if v ( x, t ) = u ( x, t )-g ( x ). What are the boundary conditions for v ? (c) Solve the equation for v ( x, t ) using separation of variables if the initial condition for u is u ( x, 0) = x 3 + x 2 . 4. Find the type, transform to normal form and solve the PDE. u xy-u xx = 0 5. Solve the PDE for u ( x, t ) using fourier transform in space: u t = cu x ,-∞ < x < ∞ u ( x, 0) = f ( x ) Write the solution as a double integral and in terms of f via inverse fourier transform....
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- Spring '07
- Math, Boundary value problem, Partial differential equation, Dirichlet boundary conditions