scholarly journals Initial boundary value problems for a system of parabolic conservation laws arising from chemotaxis in multi-dimensions

2019 ◽  
Vol 39 (7) ◽  
pp. 3789-3838 ◽  
Author(s):  
Leo G. Rebholz ◽  
◽  
Dehua Wang ◽  
Zhian Wang ◽  
Camille Zerfas ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

scholarly journals Accurate numerical schemes for approximating initial-boundary value problems for systems of conservation laws

2015 ◽  
Vol 12 (01) ◽  
pp. 61-86 ◽  
Author(s):  
Siddhartha Mishra ◽  
Laura V. Spinolo
Keyword(s):  
Conservation Laws ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Numerical Schemes ◽  
Systems Of Conservation Laws ◽  
Initial Boundary Value ◽  
Limit Solutions ◽  
Viscous Mechanism

Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standard numerical schemes for approximating conservation laws do not take into account this fact and converge to solutions that are not necessarily physically relevant. We design numerical schemes that incorporate explicit information about the underlying viscosity mechanism and approximate the physical-viscosity solution. Numerical experiments illustrating the robust performance of these schemes are presented.

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