Differential and Integral Equations
- Differential Integral Equations
- Volume 16, Number 7 (2003), 813-828.
Dynamics of parabolic equations: from classical solutions to metasolutions
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.
Differential Integral Equations, Volume 16, Number 7 (2003), 813-828.
First available in Project Euclid: 21 December 2012
Permanent link to this document
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