We introduce gradient-tempered Ginzburg-Landau, GL, free energy functional $\mathit{J}=\int \left(G\left(u_x\right)-W\left(u\right)\right)dx$, where $W\left(u\right)={\lambda }^2(2u^2-u^4)$ is the bulk energy endowed with a stiffness coefficient $a^2\left(u\right)$ which vanishes both at the phases and on the interface: $a^2\left(u\right)={\left|u\right|}^{2\gamma }{|1-u^2|}^{2\beta }$, $\frac{1}{2}<\beta ,\gamma \le 1$. It induces compact drops and interphase transitions within a finite domain. The assumed interface energy $\mathit{G}=\sqrt{1+a^2{u}_x^2}-1$, tempers the divergence of gradients in the ultra-violet limit. Consequently, when ${\lambda }^2$, the bulk energy strength parameter crosses a critical value, depending on their amplitude, the forming drops may develop at their edges sharp jumps and turn into fingers across which the energy remains finite. In the Tempered Allen-Cahn, $u_t=-\frac{\delta }{\delta x}\mathit{J}$ equation, the resulting flux-saturating diffusion delays the resolution of initial discontinuities and if $1\le \gamma$, it blocks excitation’s spread beyond its initial span. A number of explicit spherical solutions is also presented.

我们引入梯度回火 Ginzburg-Landau, GL , 自由能泛函$\mathit{J}=\int \left(G\left({你}_X\right)-宽\left(你\right)\right)dX$， 在哪里 $宽\left(你\right)={\lambda }^2(2{你}^2-{你}^4)$ 是具有刚度系数的体积能量 ${\mathrm{一种}}^2\left(你\right)$ 它在相位和界面上都消失了： ${\mathrm{一种}}^2\left(你\right)={\left|你\right|}^{2\gamma }{|1-{你}^2|}^{2\beta }$, $\frac{1}{2}<\beta ,\gamma \le 1$. 它在有限域内引起紧凑滴和相间转变。假定的界面能$\mathit{G}=\sqrt{1+{\mathrm{一种}}^2{你}_X^2}-1$，缓和紫外极限梯度的发散。因此，当${\lambda }^2$，体积能量强度参数超过临界值，取决于它们的幅度，成形液滴可能在它们的边缘急剧跳跃并变成能量保持有限的手指。在温和的 Allen-Cahn 中，${你}_{吨}=-\frac{\delta }{\delta X}\mathit{J}$ 方程，由此产生的通量饱和扩散延迟了初始不连续性的分辨率，如果 $1\le \gamma$，它阻止激发的传播超出其初始跨度。还提供了许多显式球形解决方案。