Related papers: A simple diffractive boundary value problem on an …

This is the sequel of the recent work (Du, Huang, Pu, Commun. Math. Phys, 2023, doi: 10.1007/s00220-023-04651-7) on axially symmetric gravity water waves with general vorticities, which has investigated the singular wave profile of the free…

This paper focuses on the initial- and boundary-value problem for the two-dimensional micropolar equations with only angular velocity dissipation in a smooth bounded domain. The aim here is to establish the global existence and uniqueness…

For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…

This paper is concerned with the asymptotic stability of the initial-boundary value problem of a singular PDE-ODE hybrid chemotaxis system in the half space $\R_+=[0, \infty)$. We show that when the non-zero flux boundary condition at $x=0$…

The Fast Diffusion Equation (FDE) $u_t= \Delta u^m$, with $m\in (0,1)$, is an important model for singular nonlinear (density dependent) diffusive phenomena. Here, we focus on the Cauchy-Dirichlet problem posed on smooth bounded Euclidean…

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…

The formation and propagation of singularities for Boltzmann equation in bounded domains has been an important question in numerical studies as well as in theoretical studies. Consider the nonlinear Boltzmann solution near Maxwellians under…

A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…

We study weakly stable semilinear hyperbolic boundary value problems with highly oscillatory data. Here weak stability means that exponentially growing modes are absent, but the so-called uniform Lopatinskii condition fails at some boundary…

In this paper, we mainly introduce a general method to study the existence and uniqueness of solution of free boundary problems with partially degenerate diffusion.

We study the problem of conformally deforming a manifold with boundary to have vanishing {\sigma}4-curvature in the interior and constant H4- curvature on the boundary. We prove that there are geometrically distinct solutions using…

In this paper, we study the asymptotic behavior of solutions to the initial boundary value problem for the one-dimensional compressible isentropic micropolar fluid model in a half line \mathbb{R}_{+}:=(0,\infty). We mainly investigates the…

A rarely exploited advantage of time-domain boundary integral equations compared to their frequency counterparts is that they can be used to treat certain nonlinear problems. In this work we investigate the scattering of acoustic waves by a…

The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric…

We present a novel solution procedure for initial boundary value problems. The procedure is based on an action principle, in which coordinate maps are included as dynamical degrees of freedom. This reparametrization invariant action is…

We study the perturbed sine-Gordon equation $\theta_{tt}-\theta_{xx}+\sin \theta= F(\varepsilon,x)$, where $F$ is of differentiability class $C^n$ in $\varepsilon$ and the first $k$ derivatives vanish at $0$, i.e., $\partial_\varepsilon^l…

We study a Dirichlet boundary problem related to the fractional Laplacian in a manifold. Its variational formulation arises in the study of magnitude, an invariant of compact metric spaces given by the reciprocal of the ground state energy.…

We consider Scr\"odinger equations with real-valued smooth Hamiltonians, and non-smooth bounded pseudo-differential potentials, whose symbols may be not even differentiable. The well-posedness of the Cauchy problem is proved in the frame of…

In this note we are dealing with the problem of existence and asymptotic behavior of solutions for the non-resonant singularly perturbed linear Neumann boundary value problem \begin{eqnarray*} \epsilon y"+ky=f(t),\quad k>0,\quad…

In this paper, we discuss singular Neumann boundary problem for a class of nonlinear parabolic equations in one space dimension. Our boundary problem describes motion of a planar curve sliding along the boundary with a zero contact angle,…