國立清華大學 數學系

Abstract: We proposed a simple PDE model which exhibits self-replication of spot solutions in any dimension. This model was analyzed in one and higher dimensions. In the radially symmetric case, we demonstrated that the non-existence of a ground state solution is crucial for self-replication and the conditions proposed by Nishiura and Ueyama are satisfied. In this talk, we further discuss the non-existence property of this model without the assumption of radial symmetry and show that this property is related to a critical Ding-Ni exponent of the nonlinear term in the model. Moreover we show that this critical exponent determines the oscillation behavior of the radial solutions. This is a joint work with Theodore Kolokolnikov. Tea Time: 3:30PM, R707