Two-Dimensional Hyperbolic Equations

2009 ◽  
pp. 241-325
2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chunlei Ruan ◽  
Kunfeng Liang ◽  
Xianjie Chang ◽  
Ling Zhang

Population balance equations (PBEs) are the main governing equations to model the processes of crystallization. Two-dimensional PBEs refer to the crystals that grow anisotropically with the change of two internal coordinates. Since the PBEs are hyperbolic equations, it is necessary to build up high resolution schemes to avoid numerical diffusion and numerical dispersion in order to obtain the accurate crystal size distribution (CSD). In this work, a 5th order weighted essentially nonoscillatory (WENO) method is introduced to compute the two-dimensional PBEs. Several numerical benchmark examples from literatures are carried out; it is found that WENO method has higher resolution than HR method which is well established. Therefore, WENO method is recommended in crystallization simulation when the crystal size distributions are sharp and higher accuracy is needed.


Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2599-2609
Author(s):  
B. Ahmad ◽  
A. Alsaedi ◽  
E. Cuesta ◽  
M. Kirane

For a two-dimensional time nonlinear hyperbolic equation with a power nonlinearity, a threshold exponent depending on the space dimension is presented. Furthermore, the analysis is extended not only to a system of two equations but also to a two-time fractional nonlinear equation with different time order derivatives.


2019 ◽  
pp. 187-225
Author(s):  
Victor Henner ◽  
Tatyana Belozerova ◽  
Alexander Nepomnyashchy

Author(s):  
F. Tahamtani ◽  
K. Mosaleheh ◽  
K. Seddighi

This paper is concerned with investigating the spatial decay estimates for a class of nonlinear damped hyperbolic equations. In addition, we compare the solutions of two-dimensional wave equations with different damped coefficients and establish an explicit inequality which displays continuous dependence on this coefficient.


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