论文标题
奇异的积分方程，并应用于双线非线性扩散的行进波
Singular integral equations with applications to travelling waves for doubly nonlinear diffusion
论文作者
论文摘要
我们考虑了一个奇异的伏特拉积分方程组的家族，该方程出现在单调旅行波解决方案的研究中，用于涉及$ p $ laplacian运算符的扩散连接反应方程。我们的结果扩展了由于b。\，镀金$ p = 2 $。 $ p \ neq2 $修改了积分方程中奇异性的性质，并介绍了开发一些新工具进行分析的事实。然后使用积分方程的结果来研究问题的构成函数，以双线性非线性扩散反应方程为双线性扩散反应方程的存在和特性。
We consider a family of singular Volterra integral equations that appear in the study of monotone travelling-wave solutions for a family of diffusion-convection-reaction equations involving the $p$-Laplacian operator. Our results extend the ones due to B.\,Gilding for the case $p=2$. The fact that $p\neq2$ modifies the nature of the singularity in the integral equation, and introduces the need to develop some new tools for the analysis. The results for the integral equation are then used to study the existence and properties of travelling-wave solutions for doubly nonlinear diffusion-reaction equations in terms of the constitutive functions of the problem.
