arXiv subjects

M. W. Wong

Publications and source records attributed to M. W. Wong.

2 recordsLinked to original sources

arXiv2026

Asymptotic Behavior and Error Bounds for Fisher-KPP Equations on the Real Half-Line

We study the Fisher--KPP equation on the half-line under Dirichlet,Neumann, and Robin boundary conditions. For the autonomous logistic equation, we identify bounded stationary profiles converging to $1$ and obtain exponential far-field comparison estimates. We prove local uniform convergence of nontrivial Neumann solutions to $1$. Assuming local uniform convergence of the Robin solution to its stationary profile, we derive asymptotic Neumann--Robin comparison estimates. We then consider small time-periodic Neumann and Robin boundary forcing. Under exponential stability of the homogeneous linearized semigroup, we construct a locally unique small periodic lifted mild solution and obtain a first-order expansion with a uniform $O(\varepsilon^2)$ remainder in $C_0([0,\infty))$.

math.AP↗

arXiv2017

On Dissipative Nonlinear Evolutional Pseudo-Differential Equations

First, using the uniform decomposition in both physical and frequency spaces, we obtain an equivalent norm on modulation spaces. Secondly, we consider the Cauchy problem for the dissipative evolutionary pseudo-differential equation \partial_t u + A(x,D) u = F\big((\partial^α_x u)_{|α|\leq κ}\big), \ \ u(0,x)= u_0(x), where $A(x,D)$ is a dissipative pseudo-differential operator and $F(z)$ is a multi-polynomial. We will develop the uniform decomposition techniques in both physical and frequency spaces to study its local well posedness in modulation spaces $M^s_{p,q}$ and in Sobolev spaces $H^s$. Moreover, the local solution can be extended to a global one in $L^2$ and in $H^s$ ($s>κ+d/2$) for certain nonlinearities.

math.AP↗