Differential and Integral Equations

Dynamics of parabolic equations: from classical solutions to metasolutions

Julián López-Gómez

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In this paper we describe the asymptotic behavior of the positive solutions of a class of parabolic equations according to the size of a certain parameter. Within the range of values of the parameter where the model does not admit an attracting classical steady state it possesses an attracting metasolution ---a very weak generalized solution. It turns out that the minimal metasolution attracts all positive solutions starting in a subsolution and that the limiting profile of any other positive solution lies in the order interval defined by the minimal and the maximal metasolution.

Article information

Differential Integral Equations, Volume 16, Number 7 (2003), 813-828.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35B40: Asymptotic behavior of solutions 35K20: Initial-boundary value problems for second-order parabolic equations 37L30: Attractors and their dimensions, Lyapunov exponents


López-Gómez, Julián. Dynamics of parabolic equations: from classical solutions to metasolutions. Differential Integral Equations 16 (2003), no. 7, 813--828. https://projecteuclid.org/euclid.die/1356060598

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