For the 2-D quasilinear wave equation （δt2-△x）u＋2∑i,j=0gij（δu）δiju=0 satisfying null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consid...For the 2-D quasilinear wave equation （δt2-△x）u＋2∑i,j=0gij（δu）δiju=0 satisfying null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consider a more general 2-D quasilinear wave equation （δt2-△x）u＋2∑i,j=0gij（δu）δiju=0 satisfying null conditions with small initial data and the coefficients depending simultaneously on u and δu. Through construction of an approximate solution, combined with weighted energy integral method, a quasi-global or global existence solution are established by continuous induction.展开更多
This paper is concerned with the global classical solution and the asymptotic behavior to a kind of linearly degenerate quasilinear hyperbolic system in several space variables.When the semilinear terms contain at lea...This paper is concerned with the global classical solution and the asymptotic behavior to a kind of linearly degenerate quasilinear hyperbolic system in several space variables.When the semilinear terms contain at least two waves with different propagation speeds,we can prove that the system considered admits a global classical solution by the weighted energy estimate under the small and suitable decay assumptions on the initial data.Furthermore,we can show that the solution converges to a solution of the linearized system based on the decay property of the nonlinearties.展开更多
基金partially supported by the NSFC(11571177)the Priority Academic Program Development of Jiangsu Higher Education Institutionspartially funded by the DFG through the Sino-German Project "Analysis of PDEs and Applications"
文摘For the 2-D quasilinear wave equation （δt2-△x）u＋2∑i,j=0gij（δu）δiju=0 satisfying null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consider a more general 2-D quasilinear wave equation （δt2-△x）u＋2∑i,j=0gij（δu）δiju=0 satisfying null conditions with small initial data and the coefficients depending simultaneously on u and δu. Through construction of an approximate solution, combined with weighted energy integral method, a quasi-global or global existence solution are established by continuous induction.
基金partially supported by the Outstanding Youth Fund of Zhejiang Province (Grant No. LR22A010004)the NSFC (Grant No. 12071435)。
文摘This paper is concerned with the global classical solution and the asymptotic behavior to a kind of linearly degenerate quasilinear hyperbolic system in several space variables.When the semilinear terms contain at least two waves with different propagation speeds,we can prove that the system considered admits a global classical solution by the weighted energy estimate under the small and suitable decay assumptions on the initial data.Furthermore,we can show that the solution converges to a solution of the linearized system based on the decay property of the nonlinearties.
