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Blow-up phenomena for a system of semilinear parabolic equations with nonlinear boundary conditions
, Article Mathematical Methods in the Applied Sciences ; Volume 38, Issue 3 , 2015 , Pages 527-536 ; 01704214 (ISSN) ; Hesaaraki, M ; Sharif University of Technology
John Wiley and Sons Ltd
2015
Abstract
This paper deals with the blow-up phenomena for a system of parabolic equations with nonlinear boundary conditions. We show that under some conditions on the nonlinearities, blow-up occurs at some finite time. We also obtain upper and lower bounds for the blow-up time when blow-up occurs. Copyright
Nonlinear cylindrical bending analysis of shear deformable functionally graded plates under different loadings using analytical methods
, Article International Journal of Mechanical Sciences ; Volume 50, Issue 12 , 2008 , Pages 1650-1657 ; 00207403 (ISSN) ; Haddadpour, H ; Sharif University of Technology
2008
Abstract
An exact solution is presented for the nonlinear cylindrical bending and postbuckling of shear deformable functionally graded plates in this paper. A simple power law function and the Mori-Tanaka scheme are used to model the through-the-thickness continuous gradual variation of the material properties. The von Karman nonlinear strains are used and then the nonlinear equilibrium equations and the relevant boundary conditions are obtained using Hamilton's principle. The Navier equations are reduced to a linear ordinary differential equation for transverse deflection with nonlinear boundary conditions, which can be solved by exact methods. Finally, by solving some numeral examples for simply...