Finite time blowup of multidimensional inhomogeneous isotropic Landau-Lifshitz equation on a hyperbolic space

Blowup solutions for the multidimensional isotropic inhomogeneous Landau-Lifshitz (ILL) equation on a hyperbolic n-space H2 are obtained. If the inhomogeneous terms are carefully selected, the ILL will guarantee three types of singularity solutions. Type I and type II blowup solutions of any dimensional ILL on H2 can develop a finite time singularity from smooth initial data with finite L2 energy. We prove the decay rate of energy density of the type III implicit blowup solution. If ε and C are non-zero constants, this solution develops a singularity in finite time with a local (r∈[ε,C]) finite initial energy.