A KPZ growth model with possibly unbounded data: Correctness and blow-up

Existence and uniqueness results for initial value problem with a given growth condition (upper bound) on the initial datum for the so-called generalized deterministic KPZ (Kardar–Parisi–Zhang) equation ut=uxx+λ|ux|qut=uxx+λ|ux|q are obtained. Self-similar blow-up solutions are investigated also.