The Study Of Hyperbolic Inverse Mean Curvature Flow With Forced Term

The successful application of elliptic and parabolic partial differential equations in differential geometry and physics has inspired scholars to study hyperbolic differential equation theory.Hyperbolic mean curvature flow has been widely used in the fields of crystal evolution and biomedicine and achieved many great results.On this basis,this paper studied the Cauchy problem and evolution of plane curves for hyperbolic inverse mean curvature flow with forced term.Chapter 1 introduced the research background of hyperbolic inverse mean curvature flow and the main research achievements of this paper.Chapter 2 investigated the evolution of convex plane curves for hyperbolic inverse mean curvature flow with forced term.We investigated some exact solutions and gave an example to further explain the hyperbolic inverse mean curvature flow with forced term.Chapter 4 investigated the self-similar solutions of hyperbolic inverse mean curvature flow with forced term.When the translation term disappears,we discuss the self-similar solution of the hyperbolic inverse mean curvature flow with forced term,and derive the second order nonlinear ordinary differential equation to obtain the evolution process of the plane curve under the hyperbolic inverse mean curvature flow with forced term.