带非局部源的退化半线性抛物型方程解的爆破

Blow-Up for Degenerate Semiliuear Parabolic Equations with Nonlocal Source

该文研究带Dirichlet边界条件的退化半线性抛物型方程:xqut-uxx=∫0af(u)dx,这里q>0.作者证明了局部解的存在唯一性并且得到当初值充分大时解在有限时刻爆破.进而,证明解的爆破点集是整个区间[0,a],这与具有局部源的方程解的性质不同.

In this paper, we investigate degenerate semilinear parabolic equations xqut -uxx= f0a f(u)dx with Dirichlet boundary condition and q > 0. It is proved that the local solution is existent and unique and the solution blows up in a finite time provided that the initial data u0(x) is sufficiently large. Furthermore, it is shown that the blowup set is the entire interval [0, a], which is quite different from the results for the solution with local source.