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10.1186/s40064-016-1766-8 http://scihub22266oqcxt.onion/10.1186/s40064-016-1766-8 C4769713!4769713!27026892     free     free     free Deprecated: Implicit conversion from float 209.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 209.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 209.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 209.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534       Springerplus 2016 ; 5 (ä): ä Nephropedia Template TP {{tp|p=27026892|t=2016. Perturbational blowup solutions to the compressible Euler equations with damping |pdf=|usr=}}{{27026892}} gab.com Text Perturbational blowup solutions to the compressible Euler equations with damping JO: Springerplus http://www.kidney.de/pget.php?&tw=1&pmid=27026892 #FOAvip Background: The N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions. Method: In this article, we construct two families of exact solutions for the one-dimensional isentropic compressible Euler equations with damping by the perturbational method. The two families of exact solutions found include the cases \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma >1$$\end{document}?>1 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma =1$$\end{document}?=1, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma$$\end{document}? is the adiabatic constant. Results: With analysis of the key ordinary differential equation, we show that the classes of solutions include both blowup type and global existence type when the parameters are suitably chosen. Moreover, in the blowup cases, we show that the singularities are of essential type in the sense that they cannot be smoothed by redefining values at the odd points. Conclusion: The two families of exact solutions obtained in this paper can be useful to study of related numerical methods and algorithms such as the finite difference method, the finite element method and the finite volume method that are applied by scientists to simulate the fluids for applications. Twit Text FOAVip Perturbational blowup solutions to the compressible Euler equations with damping ????Springerplus http://www.kidney.de/pget.php?&tw=1&pmid=27026892 #FOAvip Twit Text # Free Paper on # # # # # LINK http://www.kidney.de/pget.php?&tw=1&pmid=27026892 #FOAvip English Wikipedia <ref>{{Cite pmid|27026892}}</ref> Perturbational blowup solutions to the compressible Euler equations with damping #MMPMID27026892 Cheung KL Springerplus 2016[]; 5 (ä): ä PMID27026892show ga Background: The N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions. Method: In this article, we construct two families of exact solutions for the one-dimensional isentropic compressible Euler equations with damping by the perturbational method. The two families of exact solutions found include the cases \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma >1$$\end{document}?>1 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma =1$$\end{document}?=1, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma$$\end{document}? is the adiabatic constant. Results: With analysis of the key ordinary differential equation, we show that the classes of solutions include both blowup type and global existence type when the parameters are suitably chosen. Moreover, in the blowup cases, we show that the singularities are of essential type in the sense that they cannot be smoothed by redefining values at the odd points. Conclusion: The two families of exact solutions obtained in this paper can be useful to study of related numerical methods and algorithms such as the finite difference method, the finite element method and the finite volume method that are applied by scientists to simulate the fluids for applications. äPerturbational blowup solutions to the compressible Euler equations wi(epmc).pdf DeepDyve Pubget Overpricing