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Initial boundary value problem for a class of non‐linear strongly damped wave equations
Author(s) -
Zhijian Yang
Publication year - 2003
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.412
Subject(s) - mathematics , boundary value problem , mathematical analysis , class (philosophy) , galerkin method , initial value problem , stability (learning theory) , polynomial , order (exchange) , wave equation , zero (linguistics) , boundary (topology) , nonlinear system , physics , linguistics , philosophy , finance , quantum mechanics , artificial intelligence , machine learning , computer science , economics
The paper studies the existence, asymptotic behaviour and stability of global solutions to the initial boundary value problem for a class of strongly damped non‐linear wave equations. By a H00.5ptk‐Galerkin approximation scheme, it proves that the above‐mentioned problem admits a unique classical solution depending continuously on initial data and decaying to zero as t→+∞as long as the non‐linear terms are sufficiently smooth; they, as well as their derivatives or partial derivatives, are of polynomial growth order and the initial energy is properly small. Copyright © 2003 John Wiley & Sons, Ltd.