Recall that the solution of the initial-value problem \(y^\prime=ky\text{,}\) \(y(0)=A\text{,}\) is given by \(\ds y=Ae^{kx}\text{.}\) Solve the following problems ...

We study the initial boundary value problem of semilinear hyperbolic equations utt – Δu = f (u) and semilinear parabolic equations ut – Δu = f (u) with critical initial data E (0) = d (or J (u₀) = d), ...