Differential and Integral Equations

The semigroup generated by a Temple class system with large data

Paolo Baiti and Alberto Bressan

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Abstract

We consider the Cauchy problem $$ u_t+\big[F(u)\big]_x=0,\qquad u(0,x)=\bar u(x)\tag{*} $$ for a nonlinear $n\times n$ system of conservation laws with coinciding shock and rarefaction curves. Assuming the existence of a coordinates system made of Riemann invariants, we prove the existence of a weak solution of $(*)$ that depends in a Lipschitz continuous way on the initial data, in the class of functions with arbitrarily large but bounded total variation.

Article information

Source
Differential Integral Equations, Volume 10, Number 3 (1997), 401-418.

Dates
First available in Project Euclid: 2 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367525659

Mathematical Reviews number (MathSciNet)
MR1744853

Zentralblatt MATH identifier
0890.35083

Subjects
Primary: 35L65: Conservation laws
Secondary: 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]

Citation

Baiti, Paolo; Bressan, Alberto. The semigroup generated by a Temple class system with large data. Differential Integral Equations 10 (1997), no. 3, 401--418. https://projecteuclid.org/euclid.die/1367525659


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