Jingxue Yin

Grow-up rate of solutions for the heat equation with a sublinear source

In this paper, we investigate the grow-up rate of solutions for the heat equation with a sublinear source. We find that if the initial value grows fast enough, then it plays a major role in the growing up of solutions, while if the initial value grows slowly, then the sublinear source prevails. As a direct application of these results, we show that the effect of the sublinear source is negligible in the asymptotic behavior of solutions as t→∞ if the initial value grows fast enough.MSC:35K55, 35B40.

Existence and Stability of Traveling Waves for Degenerate Reaction–Diffusion Equation with Time Delay

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction–diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of

A note on the existence of time periodic solution of a superlinear heat equation

cge c^*

Critical extinction exponents for a polytropic filtration equation with absorption and source

c≥c∗ for the degenerate reaction–diffusion equation without delay, where

A note on semilinear heat equation in hyperbolic space

c^*>0

Propagation profile for a non-Newtonian polytropic filtration equation with orientated convection

c∗>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay