Abstract
We investigate the large time behavior of the global weak entropy solutions to the symmetric Keyfitz-Kranzer system with linear damping. It is proved that ast→∞the entropy solutions tend to zero in theLpnorm.
Highlights
In this paper, we consider the Cauchy problem to the symmetric system of Keyfitz-Kranzer type with linear damping ut + (uφ (r))x + au = 0, (1)Vt + (Vφ (r))x + bV = 0, with initial data u (x, 0) = u0 (x), V (x, 0) = u0 (x) . (2)This system models the propagation models of propagation of forward longitudinal and transverse waves of elastic string which moves in a plane; see [1, 2]
We investigate the large time behavior of the global weak entropy solutions to the symmetric Keyfitz-Kranzer system with linear damping
The behavior of solutions and its computation can be more complicated; for example, we consider Burger’s equation with a particular initial data and linear damping; this equation models the component of the velocity in one-dimensional flow ut with intial data u (x, 0) = {A (1 − x2), if x ∈ (−1, 1), (7)
Summary
The behavior of solutions and its computation can be more complicated; for example, we consider Burger’s equation with a particular initial data and linear damping; this equation models the component of the velocity in one-dimensional flow ut. In systems with source term, the characteristics are nonlinear functions and they could have asymptotic behavior; for example, the characteristics solutions for (6), (7) are asymptotic to the lines lim X t→∞. If the initial data (u0(x), V0(x)) ∈ L∞(R) ∩ L2(R), the Cauchy problems (1) and (2) have a weak entropy solutions satisfying.
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