TY - JOUR
T1 - Existence for wave equations on domains with arbitrary growing cracks
JF - Rend. Lincei Mat. Appl. 22 (2011) 387-408
Y1 - 2011
A1 - Gianni Dal Maso
A1 - Cristopher J. Larsen
KW - Wave equation
AB - In this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation.
PB - European Mathematical Society
UR - http://hdl.handle.net/1963/4284
U1 - 4015
U2 - Mathematics
U3 - Functional Analysis and Applications
U4 - -1
ER -