Global Classical Solutions to a Kind of Mixed Initial-Boundary Value Problem for Inhomogeneous Quasilinear Hyperbolic Systems
نویسنده
چکیده
Abstract In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant {(t, x)| t ≥ 0, x ≥ 0} is investigated. Under the assumption that the right hand side satisfies matching condition and the system is strictly hyperbolic and weakly linearly degenerate, we obtain the global existence and uniqueness of C solution and its L stability with certain small initial and boundary data.
منابع مشابه
Asymptotic behavior of global classical solutions to the mixed initial-boundary value problem for quasilinear hyperbolic systems with small BV data
In this paper, we investigate the asymptotic behavior of global classical solutions to the mixed initial-boundary value problem with small BV data for linearly degenerate quasilinear hyperbolic systems with general nonlinear boundary conditions in the half space {(t, x)|t ≥ 0, x ≥ 0}. Based on the existence result on the global classical solution, we prove that when t tends to the infinity, the...
متن کاملLife - span of classical solutions to quasilinear hyperbolic systems with slow decay initial data
In this paper the author considers the lifespan of classical solutions to Cauchy problem for general rst order quasilinear strictly hyperbolic systems in two independent variables with \slow" decay initial data. By means of constructing an example, the author rst illustrates that the classical solution to this kind of Cauchy problem may blow up in a nite time, even if system is weakly linearly ...
متن کاملGlobal solutions to hyperbolic Navier-Stokes equations
We consider a hyperbolicly perturbed Navier-Stokes initial value problem in R, n = 2, 3, arising from using a Cattaneo type relation instead of a Fourier type one in the constitutive equations. The resulting system is a hyperbolic one with quasilinear nonlinearities. The global existence of smooth solutions for small data is proved, and relations to the classical Navier-Stokes systems are discu...
متن کاملGlobal attractor for a nonlocal hyperbolic problem on ${mathcal{R}}^{N}$
We consider the quasilinear Kirchhoff's problem$$ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+f(u)=0 ,;; x in {mathcal{R}}^{N}, ;; t geq 0,$$with the initial conditions $ u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ; f(u)=|u|^{a}u$ and $(phi (x))^{-1} in L^{N/2}({mathcal{R}}^{N})cap L^{infty}({mathcal{R}}^{N} )$ is a positive function. The purpose of our work is to ...
متن کاملGlobal existence, stability results and compact invariant sets for a quasilinear nonlocal wave equation on $mathbb{R}^{N}$
We discuss the asymptotic behaviour of solutions for the nonlocal quasilinear hyperbolic problem of Kirchhoff Type [ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+delta u_{t}=|u|^{a}u,, x in mathbb{R}^{N} ,,tgeq 0;,]with initial conditions $u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ; delta geq 0$ and $(phi (x))^{-1} =g (x)$ is a positive function lying in $L^{N/2}(mathb...
متن کامل