scholarly journals An exact solution of the moving boundary problem for the relativistic plasma expansion in a dipole magnetic field

2012 ◽  
Vol 66 (7) ◽  
Author(s):  
H. B. Nersisyan ◽  
K. A. Sargsyan ◽  
D. A. Osipyan ◽  
H. H. Matevosyan
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Boundary Problem ◽  
Moving Boundary ◽  
Relativistic Plasma ◽  
Moving Boundary Problem ◽  
Plasma Expansion ◽  
Dipole Magnetic Field

Two methods to solve a fractional single phase moving boundary problem

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Xicheng Li ◽  
Shaowei Wang ◽  
Moli Zhao
Keyword(s):  
Mathematical Model ◽  
Exact Solution ◽  
Heat Equation ◽  
Fractional Derivative ◽  
Boundary Problem ◽  
Single Phase ◽  
Moving Boundary ◽  
Moving Boundary Problem ◽  
Moving Boundary Problems ◽  
Boundary Problems

AbstractA moving boundary problem of a melting problem is considered in this study. A mathematical model using the Caputo fractional derivative heat equation is proposed in the paper. Since moving boundary problems are difficult to solve for the exact solution, two methods are presented to approximate the evolution of the temperature. To simplify the computation, a similarity variable is adopted in order to reduce the partial differential equations to ordinary ones.

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