While the abstract theory available can be applied directly to problems with unbounded domains or zero boundary conditions, many problems arising in applications are in fact initial–boundary value ...

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), ...

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 ...