We construct some particular kind of solution to the two - dimensional equivariant wave map problem with inhomogeneous source term in space-time domain of type Ωα(t) = (x ∈ ℝ2: |x| α < t), where α ∈ (0, 1]. More precisely, we take the initial data (u0, u1) at time T in the space H1+ε × Hε with some ε > 0. The source term is in L1((0, T);Hε (Ωα(t))) and we show that the H1+ε - norm of the solution blows-up, when t → 0+ and α ∈ (0, 1-ε).
|Number of pages||41|
|Journal||Rendiconti dell'Istituto di Matematica dell'Universita di Trieste|
|Publication status||Published - 2003 Jan 1|
- Blow-up of solution
- Equivariant wave maps
ASJC Scopus subject areas