Uniqueness and nonuniqueness of fronts for degenerate diffusion-convection reaction equations

对流在Born-Infeld扩散模型临界前沿剖面极限形状中的作用

The role of convection in the limit shape of the critical front profile for Born-Infeld diffusion models

本文研究Born-Infeld扩散模型中引入对流项对临界前沿极限形状的影响，通过估计临界速度和分析等价一阶问题，证明不同对流项可导致极限剖面完全锐化或完全正则化，并辅以数值模拟。

Front propagation in nonlinear parabolic equations

We study existence and stability of travelling waves for nonlinear convection diffusion equations in the 1-D Euclidean space. The diffusion coefficient depends on the gradient in analogy with the p-Laplacian and may be degenerate. Unconditional stability is established with respect to initial data perturbations in the Lebesgue space of integrable functions.

Nonexistence for parabolic differential inequalities with convection terms in exterior domains

We are concerned with the nonexistence of sign-changing global weak solutions for a class of semilinear parabolic differential inequalities with convection terms in exterior domains. A weight function of the form $t^α|x|^σ$ is considered in front of the power nonlinearity. Two types of non-homogeneous boundary conditions are investigated: Neumann-type and Dirichlet-type boundary conditions. Using a unified approach, for each case, we establish sufficient criteria for the nonexistence of global weak solutions. When $α=0$, the critical exponent in the sense of Fujita is obtained. This exponent i…

Stability of travelling-wave solutions for reaction-diffusion-convection systems

We are concerned with the asymptotic behaviour of classical solutions of systems of the form u_t = Au_xx + f(u, u_x), x in R, t>0, u(x,t) a vector in RN, with u(x,0)= U(x), where A is a positive-definite diagonal matrix and f is a 'bistable' nonlinearity satisfying conditions which guarantee the existence of a comparison principle. Suppose that there is a travelling-front solution w with velocity c, that connects two stable equilibria of f. We show that if U is bounded, uniformly continuously differentiable and such that w(x) - U(x) is small when the modulus of x is large, then there exists y …

Uniform asymptotic stability for convection-reaction-diffusion equations in the inviscid limit towards Riemann shocks

The present contribution proves the asymptotic orbital stability of viscous regularizations of stable Riemann shocks of scalar balance laws, uniformly with respect to the viscosity/diffusion parameter $ε$. The uniformity is understood in the sense that all constants involved in the stability statements are uniform and that the corresponding multiscale $ε$-dependent topology reduces to the classical $W^{1,\infty}$-topology when restricted to functions supported away from the shock location. Main difficulties include that uniformity precludes any use of parabolic regularization to close regulari…

反应扩散方程锋面传播中产生的一个双重奇异边值问题的可解性

Solvability of a doubly singular boundary value problem arising in front propagation for reaction-diffusion equations

针对 $p$-Laplacian 型反应-扩散-对流方程行波研究中出现的含 $z^{-α}$ 奇性与零边值的双重奇异 ODE，本文在给定参数及连续系数条件下探讨其正解的可解性。