TY - JOUR
T1 - Global existence for a semi-discrete scheme of some quasilinear hyperbolic balance laws
AU - Yoshikawa, Shuji
AU - Kawashima, Shuichi
N1 - Funding Information:
This work was partially supported by JSPS KAKENHI Grant Numbers JP16K05234 , JP20K03687 and JP18H01131 and Grant for Basic Science Research Projects from The Sumitomo Foundation Grant Number 180823 . Authors wish to express deep gratitude to prof. Norikazu Saito for his fruitful advices and the anonymous referees for their kind advices and profound comments.
Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/6/1
Y1 - 2021/6/1
N2 - In this article, we show the global existence of solution for some semi-discrete finite difference schemes of some model system of quasilinear hyperbolic balance laws with the Cattaneo law. In [10] and [11] the first author proposed the energy method for the structure-preserving fully discrete numerical schemes for semilinear partial differential equations. The result here gives its application to quasilinear partial differential equations.
AB - In this article, we show the global existence of solution for some semi-discrete finite difference schemes of some model system of quasilinear hyperbolic balance laws with the Cattaneo law. In [10] and [11] the first author proposed the energy method for the structure-preserving fully discrete numerical schemes for semilinear partial differential equations. The result here gives its application to quasilinear partial differential equations.
KW - Hyperbolic balance law
KW - Numerical method
KW - Quasilinear evolution equation
KW - Small data global existence
KW - Structure-preserving numerical method
KW - The Cattaneo law
UR - http://www.scopus.com/inward/record.url?scp=85099273198&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85099273198&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2021.124929
DO - 10.1016/j.jmaa.2021.124929
M3 - Article
AN - SCOPUS:85099273198
SN - 0022-247X
VL - 498
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
M1 - 124929
ER -