Related papers: Infinity Laplacian equation with strong absorption…
The regular finite initial value problem at infinity is used to obtain regularity conditions on the freely specifiable parts of initial data for the vacuum Einstein equations with non-vanishing second fundamental form. These conditions…
We consider the existence of radially symmetric stationary solutions of the compressible viscous and heat-conductive polytropic ideal fluid on the unbounded exterior domain of a sphere where the boundary and far-field conditions are…
In many problems of PDE involving the Laplace-Beltrami operator on manifolds with ends, it is often useful to introduce radial or geodesic normal coordinates near infinity. In this paper, we prove the existence of such coordinates for a…
We report on recent progress in the study of nonlinear diffusion equations involving nonlocal, long-range diffusion effects. Our main concern is the so-called fractional porous medium equation, $\partial_t u +(-\Delta)^{s}(u^m)=0$, and some…
We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if the absorption is large enough, compared with the flux…
In this paper, we obtain a series of regularity results for viscosity solutions of fully nonlinear elliptic equations with oblique derivative boundary conditions. In particular, we derive the pointwise $C^{\alpha}$, $C^{1,\alpha}$ and…
Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an inviscid fluid such as the skew symmetry and the…
In this paper we address the regularity issues of drift-diffusion equation with nonlocal diffusion, where the diffusion operator is in the realm of stable-type L\'evy operator and the velocity field is defined from the considered quantity…
We consider solutions to linear parabolic equations with initial data decaying at spatial infinity. For a class of advection-diffusion equations with a spatially dependent velocity field, we study the behavior of solutions as time tends to…
In this paper, we study the boundary regularity for viscosity solutions of fully nonlinear elliptic equations. We use a unified, simple method to prove that if the domain $\Omega$ satisfies the exterior $C^{1,\mathrm{Dini}}$ condition at…
We study closed extensions A of an elliptic differential operator on a manifold with conical singularities, acting as an unbounded operator on a weighted L_p-space. Under suitable conditions we show that the resolvent (\lambda-A)^{-1}…
For the initial boundary problem of the incompressible MHD equations in a bounded domain with general curved boundary in 3D with the general Navier-slip boundary conditions for the velocity field and the perfect conducting condition for the…
In this paper, we consider the large-time behavior of solutions of a reaction diffusion system arising from a nuclear reactor model with the Robin boundary conditions, which consists of two real-valued unknown functions. In particular, we…
We show optimal existence, nonexistence and regularity results for nonnegative solutions to Dirichlet problems as $$ \begin{cases} \displaystyle -\Delta_1 u = g(u)|D u|+h(u)f & \text{in}\;\Omega,\\ u=0 & \text{on}\;\partial\Omega,…
This paper is concerned with the transient dynamics described by the solutions of the reaction-diffusion equations in which the reaction term consists of a combination of a superlinear power-law absorption and a time-independent point…
We give a short proof of almost sure invertibility of unsymmetric random Kansa collocation matrices by a class of analytic RBF vanishing at infinity, for the Poisson equation with Dirichlet boundary conditions. Such a class includes popular…
In this paper we study Liouville-type properties for a class of degenerate elliptic equations driven by the fractional infinity Laplacian with nonlinear lower-order terms, \[ \Delta_\infty^{\beta}u - c\,H(u,\nabla u) - \lambda\, f(|x|,u)=0…
This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form…
We interpret the Hilbert entropy of a convex projective structure on a closed higher-genus surface as the Hausdorff dimension of the non-differentiability points of the limit set in the full flag space $\mathcal F(\mathbb R^3)$.…
We prove that solutions to the Boltzmann equation without cut-off satisfying pointwise bounds on some observables (mass, pressure, and suitable moments) enjoy a uniform bound in $L^\infty$ in the case of hard potentials. As a consequence,…