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Blowup of solutions for a class of non‐linear evolution equations with non‐linear damping and source terms
Author(s) -
Zhijian Yang
Publication year - 2002
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.312
Subject(s) - mathematics , term (time) , class (philosophy) , linear growth , mathematical analysis , boundary value problem , compensation (psychology) , energy (signal processing) , initial value problem , linear equation , boundary (topology) , physics , statistics , psychology , quantum mechanics , artificial intelligence , computer science , psychoanalysis
We consider the blowup of solutions of the initial boundary value problem for a class of non‐linear evolution equations with non‐linear damping and source terms. By using the energy compensation method, we prove that when p >max{ m , α }, where m , α and p are non‐negative real numbers and m +1, α +1, p +1 are, respectively, the growth orders of the non‐linear strain terms, damping term and source term, under the appropriate conditions, any weak solution of the above‐mentioned problem blows up in finite time. Comparison of the results with the previous ones shows that there exist some clear condition boundaries similar to thresholds among the growth orders of the non‐linear terms, the states of the initial energy and the existence and non‐existence of global weak solutions. Copyright © 2002 John Wiley & Sons, Ltd.