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Estimates for the lifespan of solutions of an initial-boundary value problem for a nonlinear Sobolev equation with variable coefficient

Estimates for the lifespan of solutions of an initial-boundary value problem for a nonlinear... We consider an initial-boundary value problem for a nonlinear equation of Sobolev type with variable coefficient multiplying the power-law nonlinearity. We obtain sufficient conditions for both time-global and time-local solvability. In the case of local (but not global) solvability, we find two-sided estimates for the lifespan of the solution in the form of quadrature formulas and indicate special cases in which a closed form of these estimates is possible. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Estimates for the lifespan of solutions of an initial-boundary value problem for a nonlinear Sobolev equation with variable coefficient

Differential Equations , Volume 48 (6) – Jul 15, 2012

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References (5)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Pleiades Publishing, Ltd.
Subject
Mathematics; Partial Differential Equations; Difference and Functional Equations; Ordinary Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266112060031
Publisher site
See Article on Publisher Site

Abstract

We consider an initial-boundary value problem for a nonlinear equation of Sobolev type with variable coefficient multiplying the power-law nonlinearity. We obtain sufficient conditions for both time-global and time-local solvability. In the case of local (but not global) solvability, we find two-sided estimates for the lifespan of the solution in the form of quadrature formulas and indicate special cases in which a closed form of these estimates is possible.

Journal

Differential EquationsSpringer Journals

Published: Jul 15, 2012

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