论文标题
径向等效性和对一类非均匀反应扩散方程的定性理论的应用
Radial equivalence and applications to the qualitative theory for a class of non-homogeneous reaction-diffusion equations
论文作者
论文摘要
作用于径向对称解决方案对以下类别类别的非均匀反应 - 扩散方程的一些转换引入了数学作品以及在几种物理模型中。我们在这里考虑$ m \ geq1 $，$ p \ geq1 $，$ n \ geq1 $和$σ_1$，$σ_2$真实指数。一方面，我们将这些转换应用于先前的结果，以推断出径向对称解决方案的一般定性特性，另一方面，它们可以构建自相似的解决方案，这些解决方案有望成为方程动力学的模式，从而强烈改善了现有理论。我们还介绍了在半线性案例中工作的解决方案之间的映射，$ m = 1 $。
Some transformations acting on radially symmetric solutions to the following class of non-homogeneous reaction-diffusion equations $$ |x|^{σ_1}\partial_tu=Δu^m+|x|^{σ_2}u^p, \qquad (x,t)\in\real^N\times(0,\infty), $$ which has been proposed in a number of previous mathematical works as well as in several physical models, are introduced. We consider here $m\geq1$, $p\geq1$, $N\geq1$ and $σ_1$, $σ_2$ real exponents. We apply these transformations in connection to previous results on the one hand to deduce general qualitative properties of radially symmetric solutions and on the other hand to construct self-similar solutions which are expected to be patterns for the dynamics of the equations, strongly improving the existing theory. We also introduce mappings between solutions which work in the semilinear case $m=1$.
