Stiff wellposedness for hyperbolic systems with large relaxation terms (linear constantcoefficient problems)
(1997) In Advances in Differential Equations 2(4). p.643666 Abstract
 The paper deals with the Cauchy problem for the linear constantcoefficient strongly hyperbolic system $u_t+Au_x=({1}/{delta})B$.
The critical case where $B$ has a nontrivial nullspace is investigated. Under suitable assumptions on the matrices $A$ and $B$ the convergence in $L_2$ as $delta o 0$ of the solution $u(·,t,delta)$ of the Cauchy problem is proved. Then the evolution of the limit function ${check u}(·,t)$ as a solution of the Cauchy problem for the strongly hyperbolic system without zeroorder term is described. This system is called an equilibrium system and a method for obtaining it is given. A concept of stiff wellposedness is introduced that ensures solution estimates independent of $0<deltale 1$. It... (More)  The paper deals with the Cauchy problem for the linear constantcoefficient strongly hyperbolic system $u_t+Au_x=({1}/{delta})B$.
The critical case where $B$ has a nontrivial nullspace is investigated. Under suitable assumptions on the matrices $A$ and $B$ the convergence in $L_2$ as $delta o 0$ of the solution $u(·,t,delta)$ of the Cauchy problem is proved. Then the evolution of the limit function ${check u}(·,t)$ as a solution of the Cauchy problem for the strongly hyperbolic system without zeroorder term is described. This system is called an equilibrium system and a method for obtaining it is given. A concept of stiff wellposedness is introduced that ensures solution estimates independent of $0<deltale 1$. It is shown that for $2 imes 2$ systems the requirement of stiff wellposedness is equivalent to the wellknown subcharacteristic condition. The theory is illustrated by examples. One of them shows that the assumption of strong hyperbolicity is essential. Lastly, some numerical experiments for a $3 imes 3$ system are carried out. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1224357
 author
 Schroll, Achim ^{LU} and Lorenz, Jens
 organization
 publishing date
 1997
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Advances in Differential Equations
 volume
 2
 issue
 4
 pages
 643  666
 publisher
 Khayyam Publishing, Inc.
 external identifiers

 scopus:0000503001
 ISSN
 10799389
 language
 English
 LU publication?
 yes
 id
 024f397d48d34b49a2bf15b3199710be (old id 1224357)
 date added to LUP
 20160404 09:13:49
 date last changed
 20220315 18:20:40
@article{024f397d48d34b49a2bf15b3199710be, abstract = {{The paper deals with the Cauchy problem for the linear constantcoefficient strongly hyperbolic system $u_t+Au_x=({1}/{delta})B$. <br/><br> <br/><br> The critical case where $B$ has a nontrivial nullspace is investigated. Under suitable assumptions on the matrices $A$ and $B$ the convergence in $L_2$ as $delta o 0$ of the solution $u(·,t,delta)$ of the Cauchy problem is proved. Then the evolution of the limit function ${check u}(·,t)$ as a solution of the Cauchy problem for the strongly hyperbolic system without zeroorder term is described. This system is called an equilibrium system and a method for obtaining it is given. A concept of stiff wellposedness is introduced that ensures solution estimates independent of $0<deltale 1$. It is shown that for $2 imes 2$ systems the requirement of stiff wellposedness is equivalent to the wellknown subcharacteristic condition. The theory is illustrated by examples. One of them shows that the assumption of strong hyperbolicity is essential. Lastly, some numerical experiments for a $3 imes 3$ system are carried out.}}, author = {{Schroll, Achim and Lorenz, Jens}}, issn = {{10799389}}, language = {{eng}}, number = {{4}}, pages = {{643666}}, publisher = {{Khayyam Publishing, Inc.}}, series = {{Advances in Differential Equations}}, title = {{Stiff wellposedness for hyperbolic systems with large relaxation terms (linear constantcoefficient problems)}}, volume = {{2}}, year = {{1997}}, }