Unformatted text preview: , where a is a constant. (a) Is the above PDE, (i) linear, and (ii) homogeneous? Why? (b) Express g(x, y) as the product of two individual functions X(x) and Y(y) . Solve for X(x) and Y(y) , through a similar procedure to that developed in class for the heat conduction equation. What is the final form of g(x, y) ? (c) We now solve for the constants of integration, in (b) through the use of boundary/initial conditions. Given that a boundary condition is g(x=0, y) = 8 e-3y + 4 e-5y , show that the complete solution for the PDE is g(x, y)= 8 e-3(a x + y ) + 4 e-5(a x + y ) Hint: Given that there are two terms in g(x=0, y) you have to use the Principle of Superposition to write down all the possible solutions....
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- Spring '09
- Fourier Series, Periodic function, Partial differential equation, Joseph Fourier, linear homogeneous PDE