论文标题
用于Fisher型反应扩散方程的行进波，具有发散形式的通量
Traveling waves for a Fisher-type reaction-diffusion equation with a flux in divergence form
论文作者
论文摘要
考虑到其行驶波动的最小速度，抛物线运算符中传播速度的分析经常进行。该值取决于要考虑的解决方案概念。 我们分析了一类大量的Fisher型反应扩散方程，并以发散形式流动。我们使用常规流动，这可能不符合标准的椭圆状况，但没有其他类型的奇异性。 我们表明，经典行进浪移动的速度范围是右侧无限的间隔。与经典的例子相反，可能无法达到量。当流量是椭圆形或过度纤细的时，可以达到最小的传播速度。 经典的波动速度阈值通过分析一阶边界值问题的扩展来补充另一个值，而经典案例的降低了。这种奇异的最低速度可以证明是椭圆形或过椭圆流中经典最小速度的粘性极限。 我们为最小奇异速度与经典行进波动的速度之间的每个速度构建一个单数轮廓。在其他假设下，构造的轮廓可以是合理的，因为在有限变化函数框架中，启动方程的行动波。 我们还表明，即使在有界变化函数的框架中，也可能会出现饱和的前线，即使在严格较低的速度中，也可能会出现饱和的前沿。
Analysis of the speed of propagation in parabolic operators is frequently carried out considering the minimal speed at which its traveling waves move. This value depends on the solution concept being considered. We analyze an extensive class of Fisher-type reaction-diffusion equations with flows in divergence form. We work with regular flows, which may not meet the standard elliptical conditions, but without other types of singularities. We show that the range of speeds at which classic traveling waves move is an interval unbounded to the right. Contrary to classic examples, the infimum may not be reached. When the flow is elliptic or over-elliptic, the minimum speed of propagation is achieved. The classic traveling wave speed threshold is complemented by another value by analyzing an extension of the first order boundary value problem to which the classic case is reduced. This singular minimum speed can be justified as a viscous limit of classic minimal speeds in elliptic or over-elliptic flows. We construct a singular profile for each speed between the minimum singular speed and the speeds at which classic traveling waves move. Under additional assumptions, the constructed profile can be justified as that of a traveling wave of the starting equation in the framework of bounded variation functions. We also show that saturated fronts verifying the Rankine-Hugoniot condition can appear for strictly lower speeds even in the framework of bounded variation functions.
