Solvability And Initial Trace Of Heat Conduction Equation With Exponential Flow Over An Unbounded Region

In the unbounded domain,the solvability of heat conduction equations with nonlinear boundary heat flux and the study of the initial trace is one of the important directions in the study of nonlinear partial differential equation.Among the known results,the Fujita index has been developed to a relatively clear degree for the blow-up of solutions in finite moments.When we study the blow-up and global existence of solutions of initial value pairs and equations in finite time,many expressions can be obtained.The study of the solvability and the initial trace of the solution of the heat equation with exponential flow in unbounded domain is a classical subject.In this paper,the following heat conduction problems are studied,(?)with the initial condition u(x,0)=μ(x)≥0,x∈D:=R+N,where μ is a nonnegative measurable function in RN or a Radon measure in RN with suppμ (?) D.Research with exponential flow of heat conduction equation of the existence and uniqueness of nonnegative solution of the initial track,get index is a necessary condition for the existence of nonnegative solutions of the heat conduction equation and sufficient conditions for the existence of nonnegative solution,we get the sufficient conditions and necessary conditions of solutions enable us to determine the index of flow of heat conduction problem with local nonnegative solution of the initial data of the strongest singularity,and that the strongest singularity depends on whether its in (?)R+N on there.