Classification of the blow-up behavior for a semilinear wave equation with nonconstant coefficients

Asma Azaiez , Hatem Zaag (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

We consider a nonlinear wave equation with nonconstant coefficients. In particular, the coefficient in front of the second order space derivative is degenerate. We give the blow-up behavior and the regularity of the blow-up set. Of course, the main interest of the paper concerns the behavior at the origin, where the degeneracy occurs. Some nontrivial obstacles, due to the non constant speed of propagation, have to be surmounted.

Domaines: Equations aux dérivées partielles [math.AP]

Asma Azaiez, Hatem Zaag. Classification of the blow-up behavior for a semilinear wave equation with nonconstant coefficients. Annales Henri Poincaré, 2022, 24 (4), pp.1417-1437. ⟨10.1007/s00023-022-01247-0⟩. ⟨hal-02324952⟩