Use Mathematica to solve the following initial-boundary value problem: PDE: u_t = 4u_{rr} in [-T,T] x [0,\infty) u(x,0) = 0 for all x \in [-T,T] ICs: u_t(x,0) = \sin^2(x) for all x \in [-T,T] u(-T,t) = u(T,t) = 0 for all t > 0
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Define the problem: We are given the partial differential equation (PDE) u_t = 4u_{rr}, where u_t represents the partial derivative of u with respect to t, and u_{rr} represents the second partial derivative of u with respect to r. The domain of the problem is Show more…
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