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Mathematical Problems in Engineering
Volume 8, Issue 1, Pages 15-31
http://dx.doi.org/10.1080/10241230211382

Global regular solutions for the nonhomogeneous Carrier equation

1The Institute of Theoretical and Applied Mechanics, Novosibirsk 90.630090, Russia
2Department of Mathematics, Maringá State University Agencia Postal UEM, Maringá, PR 87.020-900, Brazil

Received 29 June 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study in an+1-dimensional cylinder Q global solvability of the mixed problem for the nonhomogeneous Carrier equation uttM(x,t,||u(t)||2)Δu+g(x,t,ut)=f(x,t) without restrictions on a size of initial data and f(x,t). For any natural n, we prove existence, uniqueness and the exponential decay of the energy for global generalized solutions. When n=2, we prove C(Q)-regularity of solutions.