Abstract We prove that the C^0 boundedness of solution implies the global existence and uniqueness of C^1 solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagon...Abstract We prove that the C^0 boundedness of solution implies the global existence and uniqueness of C^1 solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions.THus ,if the C^1 solution to the initial-bloundary value problem blows up in a finite time,then the solution itself must tend to the in finity at the starting point of singularity.展开更多
For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the globa...For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the global existence of H 2 classical solution to the Cauchy problem with small initial data is obtained.展开更多
The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.
文摘Abstract We prove that the C^0 boundedness of solution implies the global existence and uniqueness of C^1 solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions.THus ,if the C^1 solution to the initial-bloundary value problem blows up in a finite time,then the solution itself must tend to the in finity at the starting point of singularity.
基金supported by the Fudan University Creative Student Cultivation Program in Key Disciplinary Areas (No. EHH1411208)
文摘For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the global existence of H 2 classical solution to the Cauchy problem with small initial data is obtained.
文摘The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.