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
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.
