Related papers: The heat equation with strongly singular potential…
In this paper, we establish a H\"older-type quantitative estimate of unique continuation for solutions to the heat equation with Coulomb potentials in either a bounded convex domain or a $C^2$-smooth bounded domain. The approach is based on…
In this paper, a generalized Boussinesq equation that couples the mass and heat flows in a viscous incompressible uid is considered. The kinematic viscosity and the heat conductivity are assumed to be dependent on the temperature. The…
We study the question weather weak solutions to a class of active scalar equations, with the drift velocity and the active scalar related via a Fourier multiplier of order zero, are unique. Due to some recent results we cannot expect weak…
We show that, in general, any complex weakly nonlinear highly multimode system can reach thermodynamic equilibrium that is characterized by a unique temperature and chemical potential. The conditions leading to either positive or negative…
This article is devoted to questions concerning the existence of solutions for partial differential equation problems modeling granular flows. The models studied take into account the complex threshold rheology of these flows, as well as…
We revisit the negative energy solutions of the Dirac equation, which become relevant at very high energies and study several symmetries which follow therefrom. The consequences are briefly examined.
We derive the dynamic boundary condition for the heat equation as a limit of boundary layer problems. We study convergence of their weak and strong solutions as the width of the layer tends to zero. We also discuss $\Gamma$-convergence of…
In this paper we analyze the three-dimensional Peterlin viscoelastic model. By means of a mixed Galerkin and semigroup approach we prove the existence of a weak solutions. Further combining parabolic regularity with the relative energy…
We study the direct spectral transform for the heat equation, associated with the KP-2 equation. We show, that for real nonsingular exponentially decaying at infinity potentials the direct problem is nonsingular for arbitrary large…
Weak-scale supersymmetry is a well motivated, if speculative, theory beyond the Standard Model of particle physics. It solves the thorny issue of the Higgs mass, namely: how can it be stable to quantum corrections, when they are expected to…
We propose a Hilbert space solution theory for a nonhomogeneous heat equation with delay in the highest order derivatives with nonhomogeneous Dirichlet boundary conditions in a bounded domain. Under rather weak regularity assumptions on the…
In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a…
In this paper we give the explicit formulas for the solution of the singular generalized heat and wave equations on the Euclidian space $\R^n$.
Quantum thermodynamic quantities, normally formulated with the assumption of weak system-bath coupling (SBC), can often be contested in physical circumstances with strong SBC. This work presents an alternative treatment that enables us to…
Analytic expressions are given for the baryonic, electric and strangeness chemical potentials which explicitly show the importance of various terms. Simple scaling relations connecting these chemical potentials are found. Applications to…
The aim of this paper is to employ a strategy known from fluid dynamics in order to provide results for the linear heat equation $u_{t}-\Delta u-V(x)u=0$ in $\mathbb{R}^{n}$ with singular potentials. We show well-posedness of solutions,…
In this article, we investigate the existence and uniqueness of weak solutions to the continuous coagulation equation with collisional breakage for a class of unbounded collision kernels and distribution function. The collision kernels and…
In scattering by singular potentials $g^2U(s;r)$, the coupling constant $g^2$ is continuously decreased to zero while the stage $s$ of singularity raised simultaneously beyond all limits by some functional relation $F(g^2;s)=0$. In the…
A self-consistent determination of the spectral function and the self-energy of electrons in a hot and dense plasma is reported. The self-energy is determined within the approximation of the screened potential. It is shown, that the…
We study a wide class of solvable PT symmetric potentials in order to identify conditions under which these potentials have regular solutions with complex energy. Besides confirming previous findings for two potentials, most of our results…