Real and Complex Analysis

Reaction-diffusion waves in biology.

Evolution PDEs with Nonstandard Growth Conditions

Cauchy problems of semilinear pseudo-parabolic equations ✩

: This report summarizes mathematical research in the physical and biological sciences. Topics include: Partial differential equations; Parabolic and elliptic equations; Diffusion processes; Convective systems; Nonlinear waves; Free boundary problems.

Nonlinear Diffusion Equations.

Classical solutions for a class of fully nonlinear degenerate parabolic equations

This paper is concerned with large time behavior of solutions to the homogeneous Neumann problem of the non-Newtonian filtration equation. It is shown that the critical Fujita exponent for the problem considered is determined not only by the spatial dimension and the nonlinearity exponent, but also by the coefficient k of the first-order term. In fact, we show that there exist two thresholds k∞ and k1 on the coefficient k of the first-order term, and the critical Fujita exponent is a finite number when k is between k∞ and k1, while the critical exponent does not exist when k⩽k∞ or k⩾k1. Copyright © 2007 John Wiley & Sons, Ltd.

Critical exponent for non-Newtonian filtration equation with homogeneous Neumann boundary data

This paper deals with the large-time behaviour of solutions to the exterior problem of the non-Newtonian filtration equation with first-order term and nonlinear boundary source. In particular, the critical global exponent and the critical Fujita exponent are determined or estimated. An interesting phenomenon is shown: there exists a threshold value for the coefficient of the first-order term such that the critical global exponent is strictly less than the critical Fujita exponent when the coefficient is under this threshold, while these two exponents are identically equal when the coefficient is over this value.

Large-time behaviour of solutions to non-Newtonian filtration equations with nonlinear boundary sources

We discuss travelling wavefronts of a degenerate and singular parabolic equation in non-divergent form with changing sign sources. Necessary and sufficient conditions will be given for the existence of smooth or non-smooth and non-decreasing or non-increasing solutions. We also study the regularity of such solutions.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0308210508000231

Jingxue Yin

Papers

Classical solutions for a class of fully nonlinear degenerate parabolic equations

Critical exponent for non-Newtonian filtration equation with homogeneous Neumann boundary data

Large-time behaviour of solutions to non-Newtonian filtration equations with nonlinear boundary sources

Travelling wavefronts for a non-divergent degenerate and singular parabolic equation with changing sign sources

Shrinking self-similar solutions of a nonlinear diffusion equation with nondivergence form☆