Abstract
We derive the optimal decay rates of solution to the Cauchy problem for a set of nonlinear evolution equations with ellipticity and dissipative effects {ψt = -(1 - α)ψ - θx + αψxx, θt = -(1 - β)θ + vψx + 2ψθx + αθxx, with initial data (ψ, θ)(x, 0) = (ψ0(x), θ0(x)) → (ψ±, θ ±) as x → ±∞, where α and v are positive constants such that α < 1, v < α(1 - α), which is a special case of (1.1). We show that the solution to the system decays with the same rate to that of its associated homogenous linearized system. The main results are obtained by the use of Fourier analysis and interpolation inequality under some suitable restrictions on coefficients α and v. Moreover, we discuss the asymptotic behavior of the solution to general system (1.1) at the end.
Original language | English |
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Pages (from-to) | 399-418 |
Number of pages | 20 |
Journal | Zeitschrift fur Angewandte Mathematik und Physik |
Volume | 57 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 May 2006 |
Externally published | Yes |
Keywords
- Evolution equation
- Fourier transform
- Interpolation inequality
- Optimal decay rate
ASJC Scopus subject areas
- General Mathematics
- General Physics and Astronomy
- Applied Mathematics