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Volume 10, Issue 2
Global Smooth Solutions to a System of Dissipative Nonlinear Evolution Equations

Huaiyu Jian

J. Part. Diff. Eq., 10 (1997), pp. 158-168.

Published online: 1997-10

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  • Abstract
The existence and uniqueness are proved for global classical solutions of the following initial-boundary problem for the system of parabolic equations which is proposed by Hsieh as a substitute for the Rayleigh-Benard equation and can lead to Lorenz equations: {ψ_t = -(σ - α)ψ - σθ_x, + αψ_{xx} θ_t = -(1- β)θ + vψ_x + (ψθ)_x + βθ_{xx} ψ(0,t) = ψ(1,t) = 0, θ_x(0,t) = θ_x(1,t) = 0 ψ(x,0) = ψ_0(x), θ(x,0) = θ_0(x)
  • Keywords

System of parabolic equations nonlinear initial-boundary problem global classical solution

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@Article{JPDE-10-158, author = {Huaiyu Jian }, title = {Global Smooth Solutions to a System of Dissipative Nonlinear Evolution Equations}, journal = {Journal of Partial Differential Equations}, year = {1997}, volume = {10}, number = {2}, pages = {158--168}, abstract = { The existence and uniqueness are proved for global classical solutions of the following initial-boundary problem for the system of parabolic equations which is proposed by Hsieh as a substitute for the Rayleigh-Benard equation and can lead to Lorenz equations: {ψ_t = -(σ - α)ψ - σθ_x, + αψ_{xx} θ_t = -(1- β)θ + vψ_x + (ψθ)_x + βθ_{xx} ψ(0,t) = ψ(1,t) = 0, θ_x(0,t) = θ_x(1,t) = 0 ψ(x,0) = ψ_0(x), θ(x,0) = θ_0(x)}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5589.html} }
TY - JOUR T1 - Global Smooth Solutions to a System of Dissipative Nonlinear Evolution Equations AU - Huaiyu Jian JO - Journal of Partial Differential Equations VL - 2 SP - 158 EP - 168 PY - 1997 DA - 1997/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5589.html KW - System of parabolic equations KW - nonlinear KW - initial-boundary problem KW - global classical solution AB - The existence and uniqueness are proved for global classical solutions of the following initial-boundary problem for the system of parabolic equations which is proposed by Hsieh as a substitute for the Rayleigh-Benard equation and can lead to Lorenz equations: {ψ_t = -(σ - α)ψ - σθ_x, + αψ_{xx} θ_t = -(1- β)θ + vψ_x + (ψθ)_x + βθ_{xx} ψ(0,t) = ψ(1,t) = 0, θ_x(0,t) = θ_x(1,t) = 0 ψ(x,0) = ψ_0(x), θ(x,0) = θ_0(x)
Huaiyu Jian . (1997). Global Smooth Solutions to a System of Dissipative Nonlinear Evolution Equations. Journal of Partial Differential Equations. 10 (2). 158-168. doi:
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