The biwave maps are a class of fourth order hyperbolic equations.In this paper,we are interested in the solution formulas of the linear homogeneous biwave equations.Based on the solution formulas and the weighted ener...The biwave maps are a class of fourth order hyperbolic equations.In this paper,we are interested in the solution formulas of the linear homogeneous biwave equations.Based on the solution formulas and the weighted energy estimate,we can obtain the L∞(R^(n))−WN,1(R^(n))and L∞(R^(n))−WN,2(R^(n))estimates,respectively.By our results,we find that the biwave maps enjoy some different properties compared with the standard wave equations.展开更多
One the base of Maxwell and Dirac equations the one biquaternionic model of electro-gravimagnetic (EGM) fields is considered. The closed system of biquaternionic wave equations is constructed for determination of free...One the base of Maxwell and Dirac equations the one biquaternionic model of electro-gravimagnetic (EGM) fields is considered. The closed system of biquaternionic wave equations is constructed for determination of free system of electric and gravimagnetic charges and currents and generated by them EGM-field. By using generalized functions theory the fundamental and regular solutions of this system are determined and some of them are considered (spinors, plane waves, shock EGM-waves and others). The properties of these solutions are investigated.展开更多
基金the Zhejiang Provincial Outstanding Youth Science Foundation(Grant No.LR22A010004)the Natural Science Foundation of Zhejiang Province(Grant No.LY20A010026)the National Natural Science Foundation of China(Grant Nos.12071435 and 11871212).
文摘The biwave maps are a class of fourth order hyperbolic equations.In this paper,we are interested in the solution formulas of the linear homogeneous biwave equations.Based on the solution formulas and the weighted energy estimate,we can obtain the L∞(R^(n))−WN,1(R^(n))and L∞(R^(n))−WN,2(R^(n))estimates,respectively.By our results,we find that the biwave maps enjoy some different properties compared with the standard wave equations.
文摘One the base of Maxwell and Dirac equations the one biquaternionic model of electro-gravimagnetic (EGM) fields is considered. The closed system of biquaternionic wave equations is constructed for determination of free system of electric and gravimagnetic charges and currents and generated by them EGM-field. By using generalized functions theory the fundamental and regular solutions of this system are determined and some of them are considered (spinors, plane waves, shock EGM-waves and others). The properties of these solutions are investigated.
