SIAM Journal on Mathematical Analysis

This paper deals with the two species cancer invasion haptotaxis model $c_{1t}=\Delta c_1-\chi_1\nabla\cdot(c_1\nabla v)-\mu_{EMT}c_1+\mu_1c_1(r_1-c_1-c_2-v);\;c_{2t}=\Delta c_2-\chi_2\nabla\cdot(c_2\nabla v)+\mu_{EMT}c_1+ \mu_2c_2(r_2-c_1-c_2-v);\;\tau m_...

We introduce Robin boundary conditions for biharmonic operators, which are a model for elastically supported plates and are closely related to the study of spaces of traces of Sobolev functions. We study the dependence of the operator, its eigenvalues, ...

In this paper, we prove that in bounded planar domains with $C^{2,\alpha}$ boundary, for almost every initial condition in the sense of the Lebesgue measure, the point vortex system has a global solution, meaning that there is no collision between two ...

This paper is concerned with the sharp interface limit for the Allen--Cahn equation with a nonlinear Robin boundary condition in a bounded smooth domain $\Omega\subset\R^2$. We assume that a diffuse interface already has developed and that it is in ...

We consider the focusing energy critical nonlinear Schrödinger equation (NLS) with inverse square potential in dimension $d= 3, 4, 5$ with the details given in $d=3$ and remarks on results in other dimensions. Solutions on an energy surface of the ground ...

We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities, while at the same time ...

The paper gives a comprehensive study of inertial manifolds for semilinear parabolic equations and their smoothness using the spatial averaging method suggested by Sell and Mallet-Paret. We present a universal approach which covers the most part of ...

We consider the Kirchhoff equation $\partial_{tt} u - \Delta u \big( 1 + \int_{\mathbb{T}^d} |\nabla u|^2 \big) = 0$ on the $d$-dimensional torus $\mathbb{T}^d$, and its Cauchy problem with initial data $u(0,x)$, $\partial_t u(0,x)$ of size $\varepsilon$ ...

This article constructs a surface whose Neumann--Poincaré (NP) integral operator has infinitely many eigenvalues embedded in its essential spectrum. The surface is a sphere perturbed by smoothly attaching a conical singularity, which imparts the essential ...

In this paper, we mainly focus on radial transonic solutions for the steady hydrodynamic model of semiconductors represented by Euler--Poisson equations with sonic boundary in $n$ dimensions. In an annulus domain, given constant electronic current $j_0$ ...

Let $\mu_2(\Omega)$ be the first positive eigenvalue of the Neumann Laplacian in a bounded domain $\Omega \subset \mathbb{R}^N$. It was proved by Szegö for $N=2$ and by Weinberger for $N \geq 2$ that among all equimeasurable domains $\mu_2(\Omega)$ attains ...

In this paper we characterize the regularity structure, as well as show the global-in-time existence and uniqueness, of (energy) conservative solutions to the Hunter--Saxton equation by using the method of characteristics. The major difference between the ...

Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for studying biological systems involving both noise in the reaction process and diffusive transport. In this work we derive coarse-grained deterministic partial integro-...

The half-space matching (HSM) method has recently been developed as a new method for the solution of two-dimensional scattering problems with complex backgrounds, providing an alternative to perfectly matched layers or other artificial boundary ...

Equilibrium models based on a free energy functional deserve special interest in recent investigations, as their critical points exhibit various pattern structures. These systems are characterized by the presence of coexisting phases, whose distribution ...

We develop novel first-kind boundary integral equations for Euclidean Dirac operators in 3-dimensional Lipschitz domains comprising square-integrable potentials and involving only weakly singular kernels. Generalized G\aarding inequalities are derived and ...

We study the steady creep flow of a perfectly viscoplastic solid comprising a small volume fraction of fibers with high viscosity contrast. Our study unveils new effects related to anisotropy and conditioned by the Norton exponent and the shape of the ...

We consider classical solutions to the three-dimensional Vlasov--Poisson system with a radiation reaction term. When the smooth initial data have bounded second order velocity-spatial (or velocity) moments and satisfy some decay conditions, by ...

We study the linear stability of entire radial solutions $u(re^{i\theta})=f(r)e^{i\theta}$, with positive increasing profile $f(r)$, to the anisotropic Ginzburg--Landau equation $-\Delta u -\delta (\partial_x+i\partial_y)^2\bar u =(1-|u|^2)u,\ -1<\delta <1$...

We study a diffuse interface model describing the evolution of the flow of a binary fluid in a Hele-Shaw cell. The model consists of a Cahn--Hilliard--Darcy type system with transport and mass source. A relevant physical application is related to tumor ...

We investigate the existence of ground states with prescribed mass for the NLS energy with combined $L^2$-critical and subcritical nonlinearities, on a general noncompact metric graph $\mathcal G$. The interplay between the different nonlinearities ...

In this article, we consider a class of strictly hyperbolic triangular systems involving a transport equation. Such systems are known to create measure solutions for the initial value problem. Adding a stronger transversality assumption on the fields, we ...

We prove global existence of weak solutions for a version of the one velocity Baer--Nunziato system with dissipation describing a mixture of two noninteracting viscous compressible fluids in a piecewise regular Lipschitz domain with general inflow/outflow ...

Nondominated sorting is a discrete process that sorts points in Euclidean space according to the coordinatewise partial order and is used to rank feasible solutions to multiobjective optimization problems. It was previously shown that nondominated sorting ...

We establish the existence, uniqueness, and stability of subsonic flows past an airfoil with a vortex line at the trailing edge. Such a flow pattern is governed by the two-dimensional steady compressible Euler equations. The vortex line attached to the ...

In this paper we construct particular solutions to the classical Vlasov--Poisson system near stable Penrose initial data on ${\mathbb T} \times {\mathbb{R}}$ that are a combination of elementary waves with arbitrarily high frequencies. These waves ...

A maximum entropy dissipation problem at a traffic junction and the corresponding coupling condition are studied. We prove that this problem is equivalent to a coupling condition introduced by Holden and Risebro. An $L^1$-contraction property of the ...

We consider two-dimensional Schrödinger equations with honeycomb potentials and slow time-periodic forcing of the form $i\psi_t (t,{x}) = H^\varepsilon(t)\psi=\left(H^0+2i\varepsilon A (\varepsilon t) \cdot \nabla \right)\psi, H^0=-\Delta +V ({x})$. The ...

In this paper, we justify the semiclassical limit of the Gross--Pitaevskii equation with Dirichlet boundary condition on the three-dimensional upper space under the assumption that the leading-order terms to both initial amplitude and initial phase ...

We consider a particle bound to a two-dimensional plane and a double-well potential, subject to a perpendicular uniform magnetic field. The energy difference between the lowest two eigenvalues---the eigenvalue splitting---is related to the tunneling ...