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The relationships between some types of partial differential equations and ordinary differential equations as well as their applications
Author(s) -
Song Xianfa,
Lv Xiaoshuang
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4741
Subject(s) - mathematics , first order partial differential equation , separable partial differential equation , partial differential equation , ordinary differential equation , stochastic partial differential equation , mathematical analysis , exact differential equation , method of characteristics , differential equation , exponential integrator , parabolic partial differential equation , numerical partial differential equations , integrating factor , differential algebraic equation
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.