Kirchhoff equations in \(B^k_{\Delta}\) classes (Q1958668)

The author studies the global solvability of the Cauchy problem for the Kirchhoff equation with non-ultradifferentiable initial data and forcing term. More precisely, he introduces the subclass \(B^k_\Delta\) of \[ H^{1+{k\over 2}}\times H^{{k\over 2}}\times L^1_{\text{loc}}([0,\infty); H^{{k\over 2}}) \] and proves for \(k= 1,2\) global existence and uniqueness result for each \((\phi,\psi,f)\in B^k_\Delta\), \(\phi\), \(\psi\) being the corresponding initial data and \(f\) -- the forcing term. It is interesting to point out that J\(B^k_\Delta\) \((k\geq 1)\) do not contain nonzero compactly supported functions.