The relationships between some types of partial differential equations and ordinary differential equations as well as their applications

Abstract

In this article, we establish some relationships between several types of partial differential equations and ordinary differential equations. One application of these relationships is that we can get the exact values of the blowup time and the blowup rate of the solution to a partial differential equation by solving an ordinary differential equation. Another application of these relationships is that we can give the estimates for the spatial integration (or mean value) of the solution to a partial differential equation. We also obtain the lower and upper bounds for the blowup time of the solution to a parabolic equation with weighted function and space‐time integral in the nonlinear term.

Nonindependent Session Recommendation Based on Ordinary Differential Equation

“…e original intent of this approach was to model the user's nonindependent intent. In other words, we can get the potential trajectory at any point in time by solving the Ordinary Differential Equations [24], which allows us to make forward or backward predictions at any point in time. e contributions of this work are as follows:…”