<abstract xmlns="http://www.w3.org/1999/xhtml">Let Ω be a bounded domain in <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/auom-2016-0060_001.jpg"></inline-graphic> with smooth boundary, and let 𝓧1; 𝓧2; · · ·, 𝓧m be points in Ω. We are concerned with the singular stationary non-homogenous q-Kuramoto-Sivashinsky eaquation (q-KSE:<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/auom-2016-0060_002.jpg"></inline-graphic>where we use some nonlinear domain decomposition method to give a suficient condition to have a positive weak solution u in Ω under the physical Dirichlet-like boundary conditions <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/auom-2016-0060_003.jpg"></inline-graphic>, which is singular at each 𝓧i as the parameters λ, ϒ and ρ tend to 0 and where q ∈ [1, 4] is a real number.</abstract>

Let Ω be a bounded domain in  with smooth boundary, and let 𝓧1; 𝓧2; · · ·, 𝓧m be points in Ω. We are concerned with the singular stationary non-homogenous q-Kuramoto-Sivashinsky eaquation (q-KSE:where we use some nonlinear domain decomposition method to give a suficient condition to have a positive weak solution u in Ω under the physical Dirichlet-like boundary conditions , which is singular at each 𝓧i as the parameters λ, ϒ and ρ tend to 0 and where q ∈ [1, 4] is a real number.

Singular Limits for 4-Dimensional General Stationary Q-Kuramoto-Sivashinsky Equation (Q-Kse) with Exponential Nonlinearity

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Let Ω be a bounded domain in  with smooth boundary, and let 𝓧1; 𝓧2; · · ·, 𝓧m be points in Ω. We are concerned with the singular stationary non-homogenous...

Singular Limits for 4-Dimensional General Stationary Q-Kuramoto-Sivashinsky Equation (Q-Kse) with Exponential Nonlinearity

Published Online: Sep 21, 2017

Page range: 295 - 337

Received: Oct 03, 2015

Accepted: Dec 16, 2015

DOI: https://doi.org/10.1515/auom-2016-0060

Keywords
Singular limits, Green's function, Kuramoto-Sivashinsky equation, Exponential nonlinearity, Nonlinear domain decomposition method.

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Singular Limits for 4-Dimensional General Stationary Q-Kuramoto-Sivashinsky Equation (Q-Kse) with Exponential Nonlinearity

Published Online: Sep 21, 2017

Page range: 295 - 337

Received: Oct 03, 2015

Accepted: Dec 16, 2015

DOI: https://doi.org/10.1515/auom-2016-0060

KeywordsSingular limits, Green's function, Kuramoto-Sivashinsky equation, Exponential nonlinearity, Nonlinear domain decomposition method.

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Singular limits, Green's function, Kuramoto-Sivashinsky equation, Exponential nonlinearity, Nonlinear domain decomposition method.