TY - JOUR
T1 - Local boundedness of weak solutions to the Diffusive Wave Approximation of the Shallow Water equations
AU - Singer, Thomas
AU - Vestberg, Matias
PY - 2019/3/5
Y1 - 2019/3/5
N2 - In this paper we prove that weak solutions to the Diffusive Wave Approximation of the Shallow Water equations ∂tu−∇⋅((u−z)α|∇u|γ−1∇u)=f are locally bounded. Here, u describes the height of the water, z is a given function that represents the land elevation and f is a source term accounting for evaporation, infiltration or rainfall.
AB - In this paper we prove that weak solutions to the Diffusive Wave Approximation of the Shallow Water equations ∂tu−∇⋅((u−z)α|∇u|γ−1∇u)=f are locally bounded. Here, u describes the height of the water, z is a given function that represents the land elevation and f is a source term accounting for evaporation, infiltration or rainfall.
KW - Doubly nonlinear parabolic equations
KW - Local boundedness
UR - http://www.scopus.com/inward/record.url?scp=85054062526&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2018.08.051
DO - 10.1016/j.jde.2018.08.051
M3 - Article
SN - 0022-0396
VL - 266
SP - 3014
EP - 3033
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 6
ER -