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| Some Coneral Results on the First Boundry Value Problem forQuasiliear Degenerate Parabolic Equation |
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Citation： |
Wu Zhuoqun,Zhao Junning.Some Coneral Results on the First Boundry Value Problem forQuasiliear Degenerate Parabolic Equation[J].Chinese Annals of Mathematics B,1983,4(3):319~328 |
| Page view： 815
Net amount： 764 |
Authors： |
Wu Zhuoqun; Zhao Junning |
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| Abstract： |
In this paper, the authors investigate the first boundary value problem for equations of the form
$\[Lu = \frac{{\partial u}}{{\partial t}} - \frac{\partial }{{\partial {x_i}}}({a^{ij}}(u,x,t)\frac{{\partial u}}{{\partial {x_j}}}) - \frac{{\partial {f^i}(u,x,t)}}{{\partial {x_i}}} = g(u,x,t)\]$
with $a^ij(u,x,t)\xi_i\xi_j\geq 0$
An existence theorem of solution in BV_1,1/2(Q_T) is proved. The principal condition is that there exists \delta>0 such that for any (x, t)\in Q_T,|u|\geq M
$a^ij(u,x,t)\xi_i\xi_j-\delta\sum\limits_i,j=1^m(a_x^ij(u,x,t)\xi_i)^2\geq 0$ |
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