Admissible solutions for a class of nonlinear parabolic problems with non-negative data
Admissible solutions for a class of nonlinear parabolic problems with non-negative data
复制标题
DOI：
10.1017/s0308210500001153
复制
发表时间：
2001-08
期刊：
影响因子：
--
通讯作者：
E. Feireisl;H. Petzeltová;F. Simondon
中科院分区：
文献类型：
--
作者：
E. Feireisl;H. Petzeltová;F. Simondon
对于粘性解理论不适用的抛物型方程，我们定义了一类新的容许解。一个典型的例子是多孔介质方程补充低阶项，非线性的梯度。在这种情况下，方程中的非线性在粘性溶液理论的意义上是不恰当的。容许的解决方案满足一个非常普遍的比较原则，因此，相应的初边值问题在这类适定性。只要方程中的非线性适当，它们与标准粘度解是一致的。
We define a new class of admissible solutions for the parabolic problems where the theory of viscosity solutions does not apply. A typical example is the porous medium equation complemented by lower-order terms, nonlinear with respect to the gradient. In the case, the nonlinearity in the equation fails to be proper in the sense of the theory of viscosity solutions. The admissible solutions satisfy a very general comparison principle and, consequently, the corresponding initial-boundary value problems are well-posed in this class. They coincide with the standard viscosity solutions provided the nonlinearity in the equation is proper.