Related papers: On a parabolic operator of dissipative systems

In this paper, we investigate superintegrable systems which separate in parabolic coordinates and admit a third-order integral of motion. We give the corresponding determining equations and show that all such systems are multi-separable and…

We study the operator $L=-\Delta+q$ on a bounded domain $\Omega\subset\mathbb R^n$, where $q(x)$ is a distributional potential. We find sufficient conditions for $q(x)$ which guarantee that $L$ is well--defined with Dirichlet and…

In this paper we are interested in integro-differential elliptic and parabolic equations involving nonlocal operators with order less than one, and a gradient term whose coercivity growth makes it the leading term in the equation. We obtain…

Aim of this paper is the qualitative analysis of the solution of a boundary value problem for a third-order non linear parabolic equation which describes several dissipative models. When the source term is linear, the problem is explictly…

In the present paper we consider the Dirichlet problem for the second order differential operator $E=\nabla(A \nabla)$,where $A$ is a matrix with complex valued $L^\infty$ entries. We introduce the concept of dissipativity of $E$ with…

Let ${X_j},{Y_j}(j = 1, \cdot \cdot \cdot,n)$ be vector fields satisfying H\"{o}rmander's condition and ${\Delta_L} = \sum\limits_{j = 1}^n {(X_j^2 + Y_j^2)}$. In this paper, we establish some inequalities of Dirichlet eigenvalues for…

In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in $N-$dimensional domains $\Omega$. We also consider singular and degenerate elliptic problems with $A_p$ coefficients involving the…

This paper is devoted to the construction of exponential integrators of first and second order for the time discretization of constrained parabolic systems. For this extend, we combine well-known exponential integrators for unconstrained…

We develop the machinery of boundary triplets for one-dimensional operators generated by formally self-adjoint quasi-differential expression of arbitrary order on a finite interval. The technique are then used to describe all maximal…

It is shown that the theory of real symmetric second-order elliptic operators in divergence form on $\Ri^d$ can be formulated in terms of a regular strongly local Dirichlet form irregardless of the order of degeneracy. The behaviour of the…

We study higher-order elliptic operators on one-dimensional ramified structures (networks). We introduce a general variational framework for fourth-order operators that allows us to study features of both hyperbolic and parabolic equations…

This paper is concerned with spectral estimates for the first Dirichlet eigenvalue of the degenerate $p$-Laplace operator in bounded simply connected domains $\Omega \subset \mathbb C$. The proposed approach relies on the conformal analysis…

We consider the Dirichlet problem Lu = 0 in D u = g on E = boundary of D for two second order elliptic operators L_k(u) = \sum_{i,j=1}^n a_k^{ij}(x) \partial_{ij} u(x), k=0,1, in a bounded Lipschitz domain D in R^n. The coefficients…

We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading…

In this paper, exploiting variational methods, the existence of three weak solutions for a class of elliptic equations involving a general operator in divergence form and with Dirichlet boundary condition is investigated. Several special…

Let $\mathcal{O} \subset \mathbb{R}^d$ be a bounded domain of class $C^2$. In the Hilbert space $L_2(\mathcal{O};\mathbb{C}^n)$, we consider a matrix elliptic second order differential operator $\mathcal{A}_{D,\varepsilon}$ with the…

We show that elliptic second order operators $A$ of divergence type fulfill maximal parabolic regularity on distribution spaces, even if the underlying domain is highly non-smooth, the coefficients of $A$ are discontinuous and $A$ is…

This paper is devoted to the study of the Dirichlet problem for the parabolic equation driven by the $1$--Laplacian operator under minimal integrability assumptions. Specifically, we consider \begin{equation*} u'-\Div(Du/|D…

Consider the one-dimensional elliptic operator given by \begin{equation*} (L_\epsilon f)(x) \;=\; b (x) \, f'(x) \,+\, \epsilon\, a (x)\, f''(x) \;, \end{equation*} where the drift $b\colon R \to R$ and the diffusion coefficient $a\colon R…

A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…