Analysis of dynamic singularities in nonlinear evolution equations

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In this project, we studied the qualitative properties of solutions with moving singularities for various nonlinear parabolic partial differential equations. First, we investigated conditions for the global existence of solutions with singularities. Next, under certain conditions, the solution converges to a singular steady state. Furthermore, we showed that the convergence rate depends on the decay rate of initial values. This implies that there are two types of singular steady states that arecharacterized by the convergence rate.