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Nonlinear Source (nonlinear + source)

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Mathematics and Statistics100%

Selected Abstracts

Blow up for a Cauchy viscoelastic problem with a nonlinear dissipation of cubic convolution type

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2009
Shengqi Yu
Abstract In this paper, we consider a Cauchy viscoelastic problem with a nonlinear source of polynomial type and a nonlinear dissipation of cubic convolution type involving a singular kernel. Under suitable conditions on the initial data and the relaxation functions, it is proved that the solution of this particular problem blows up in finite time. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Numerical blow-up for the porous medium equation with a source

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2004
Raśl Ferreira
Abstract We study numerical approximations of positive solutions of the porous medium equation with a nonlinear source, where m > 1, p > 0 and L > 0 are parameters. We describe in terms of p, m, and L when solutions of a semidiscretization in space exist globally in time and when they blow up in a finite time. We also find the blow-up rates and the blow-up sets, proving that there is no regional blow-up for the numerical scheme. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 [source]

Localization for a doubly degenerate parabolic equation with strongly nonlinear sources

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2010
Zhaoyin Xiang
Abstract In this paper, we study the strict localization for the doubly degenerate parabolic equation with strongly nonlinear sources, We prove that, for non-negative compactly supported initial data, the strict localization occurs if and only if q,m(p,1). Copyright © 2009 John Wiley & Sons, Ltd. [source]