CAJ | 학술논문

Keldysh方程是在研究跨音速管道流问题时导出的一个简化的数学模型，也是研究混合型偏微分方程模型的一个典型代表。对于其含有非零源项的退化双曲部分的初值问题，本文利用部分Fourier变换与ODE求解的办法给出了相应线性方程解的一个显式表达式及其全局一致估计，并在这个估计的基础上利用不动点定理建立了一类半线性问题的解的全局存在性。同时给出了解的奇性传播可以仅沿一支特征线传播的一个例子。
Keldysh방정시재연구과음속관도류문제시도출적일개간화적수학모형，야시연구혼합형편미분방정모형적일개전형대표。대우기함유비령원항적퇴화쌍곡부분적초치문제，본문이용부분Fourier변환여ODE구해적판법급출료상응선성방정해적일개현식표체식급기전국일치고계，병재저개고계적기출상이용불동점정리건립료일류반선성문제적해적전국존재성。동시급출료해적기성전파가이부연일지특정선전파적일개례자。
Keldysh equation is a mathematical model which was derived in studying fluid dynamics,and also is a typical example of mixed type partial differential equations. For the initial value problem of its degenerate hyperbolic part with nonzero source term,we find a solution by use of partial Fourier transformation and ODE’s method,and then derive its a global uniform estimate. Based on it and the fixed point theorem,we establish the global existence for solution of a class of semilinear problem. Meanwhile,we find an example to desmontrate the propogation of singularity which is only along one of the characteristics.