Admissibility Criteria and Admissible Weak Solutions of Riemann Problems for Conservation Laws of Mixed Type: A Summary

1990 ◽  
pp. 85-88
Author(s):  
L. Hsiao
Keyword(s):  
Conservation Laws ◽  
Weak Solutions ◽  
Mixed Type ◽  
Type A ◽  
Riemann Problems

scholarly journals On a degenerate parabolic equation with Newtonian fluid∼non-Newtonian fluid mixed type

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sujun Weng
Keyword(s):  
Parabolic Equation ◽  
Newtonian Fluid ◽  
Weak Solutions ◽  
Mixed Type ◽  
Degenerate Parabolic Equation ◽  
Type Equation ◽  
Existence Of Weak Solutions ◽  
Degenerate Parabolic ◽  
The Stability ◽  
Increasing Function

AbstractWe study the existence of weak solutions to a Newtonian fluid∼non-Newtonian fluid mixed-type equation $$ {u_{t}}= \operatorname{div} \bigl(b(x,t){ \bigl\vert {\nabla A(u)} \bigr\vert ^{p(x) - 2}}\nabla A(u)+\alpha (x,t)\nabla A(u) \bigr)+f(u,x,t). $$ u t = div ( b ( x , t ) | ∇ A ( u ) | p ( x ) − 2 ∇ A ( u ) + α ( x , t ) ∇ A ( u ) ) + f ( u , x , t ) . We assume that $A'(s)=a(s)\geq 0$ A ′ ( s ) = a ( s ) ≥ 0 , $A(s)$ A ( s ) is a strictly increasing function, $A(0)=0$ A ( 0 ) = 0 , $b(x,t)\geq 0$ b ( x , t ) ≥ 0 , and $\alpha (x,t)\geq 0$ α ( x , t ) ≥ 0 . If $$ b(x,t)=\alpha (x,t)=0,\quad (x,t)\in \partial \Omega \times [0,T], $$ b ( x , t ) = α ( x , t ) = 0 , ( x , t ) ∈ ∂ Ω × [ 0 , T ] , then we prove the stability of weak solutions without the boundary value condition.

Asymptotic equations for conservation laws of mixed type

Wave Motion ◽  
1992 ◽  
Vol 16 (1) ◽  
pp. 57-64 ◽  
Author(s):  
Moysey Brio ◽  
John K. Hunter
Keyword(s):  
Conservation Laws ◽  
Mixed Type ◽  
Asymptotic Equations

scholarly journals A Note on Weak Solutions of Conservation Laws and Energy/Entropy Conservation

2018 ◽  
Vol 229 (3) ◽  
pp. 1223-1238 ◽  
Author(s):  
Piotr Gwiazda ◽  
Martin Michálek ◽  
Agnieszka Świerczewska-Gwiazda
Keyword(s):  
Conservation Laws ◽  
Weak Solutions ◽  
Energy Entropy ◽  
Entropy Conservation

ABOUT UNIQUENESS OF WEAK SOLUTIONS TO FIRST ORDER QUASI-LINEAR EQUATIONS

2002 ◽  
Vol 12 (11) ◽  
pp. 1599-1615 ◽  
Author(s):  
J. NIETO ◽  
J. SOLER ◽  
F. POUPAUD
Keyword(s):  
Conservation Laws ◽  
Weak Solutions ◽  
Entropy Solution ◽  
Linear Equations ◽  
Particle Method ◽  
Entropy Condition ◽  
First Order

In this paper we give a criterion to discriminate the entropy solution to quasi-linear equations of first order among weak solutions. This uniqueness statement is a generalization of Oleinik's criterion, which makes reference to the measure of the increasing character of weak solutions. The link between Oleinik's criterion and the entropy condition due to Kruzhkov is also clarified. An application of this analysis to the convergence of the particle method for conservation laws is also given by using the Filippov characteristics.

Conservation Laws of Mixed Type Describing Three-Phase Flow in Porous Media

1986 ◽  
Vol 46 (6) ◽  
pp. 1000-1017 ◽  
Author(s):  
John B. Bell ◽  
John A. Trangenstein ◽  
Gregory R. Shubin
Keyword(s):  
Porous Media ◽  
Conservation Laws ◽  
Mixed Type ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Three Phase ◽  
Three Phase Flow
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