scholarly journals Initial and Boundary Value Problem for a System of Balance Laws from Chemotaxis: Global Dynamics and Diffusivity Limit

2021 ◽  
Vol 37 (1) ◽  
pp. 61-110
Author(s):  
Zefu Feng
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Global Dynamics ◽  
Balance Laws ◽  
System Of Balance Laws

Definitions of solutions to the IBVP for multi-dimensional scalar balance laws

2018 ◽  
Vol 15 (02) ◽  
pp. 349-374 ◽  
Author(s):  
Elena Rossi
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
General Framework ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Balance Laws ◽  
Initial Boundary Value

We consider four definitions of solution to the initial-boundary value problem (IBVP) for a scalar balance laws in several space dimensions. These definitions are extended to the same most general framework and then compared. The first aim of this paper is to detail differences and analogies among them. We focus then on the ways the boundary conditions are fulfilled according to each definition, providing also connections among these various modes. The main result is the proof of the equivalence among the presented definitions of solution.

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