\(L^1\) stability of patterns of non-interacting large shock waves (Q2733842)
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scientific article; zbMATH DE number 1633095
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^1\) stability of patterns of non-interacting large shock waves |
scientific article; zbMATH DE number 1633095 |
Statements
12 August 2001
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Lipschitz semigroup
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\(L^1\) stability of patterns of non-interacting large shock waves (English)
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The author deals with a strictly hyperbolic system of conservation laws in 1D, that is NEWLINE\[NEWLINE\begin{cases} u_t+f(u)_x=0,\\ u(0,x)=u_0(x),\quad u_0(x) \text{ is real-valued}.\end{cases} \tag{1}NEWLINE\]NEWLINE The goal of this paper is to treat (1) if \(u_0(x)\) is a small perturbation of the corresponding Riemann problem. Under a suitable finiteness condition the problem (1) has a unique solution defined globally in space and time, while a stronger stability condition guarantees the existence of a Lipschitz semigroup of the solutions.
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