相关论文: Decaying positive global solutions of second order…
We study the existence and multiplicity of solutions and the global solution curve of the following free boundary value problem, arising in plasma physics, see R. Temam [18], and H. Berestycki and H. Brezis [3]: find a function $u(x)$ and a…
Consider an operator equation (*) $B(u)-f=0$ in a real Hilbert space. Let us call this equation ill-posed if the operator $B'(u)$ is not boundedly invertible, and well-posed otherwise. The DSM (dynamical systems method) for solving equation…
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…
The aim of this note is to present preliminary existence results for a system of cross-diffusion equations defined on a domain with moving boundaries, which model the evolution of the concentrations of different chemical species in a solid…
Initial-boundary value problems for the 2D Zakharov-Kuznetsov equation posed on bounded rectangles and on a strip are considered. Spectral properties of a linearized operator and critical sizes of domains are studied. Exponential decay of…
A condition which guaranties the exponential decay of the solutions of the initial-boundary value problem for the damped wave equation is proved. A method for the effective computability of the coefficient of exponential decay is also…
Let $\Omega$ be a smooth bounded domain in $\mathbb{R}^n$ ($n\geq 3$) such that $0\in\partial \Omega$. In this memoir, we consider issues of non-existence, existence, and multiplicity of variational solutions in $H_{1,0}^2(\Omega)$ for the…
Over a bounded strictly convex domain in $\mathbb{R}^n$ with smooth boundary, we establish a priori gradient estimate for an anisotropic mean curvature flow with prescribed contact angle and Neumann boundary conditions. The estimates…
The paper presents theorems on the calculation of the index of a singular point and at the infinity of monotone type mappings. These theorems cover basic cases when the principal linear part of a mapping is degenerate. Applications of these…
A new boundary value problem for partial differential equations is discussed. We consider an arbitrary solution of an elliptic or parabolic equation in a given domain and no boundary conditions are assumed. We study which restrictions the…
We consider the semilinear heat equation with a superlinear nonlinearity and we study the properties of threshold or subthreshold solutions, lying on or below the boundary between blow-up and global existence, respectively. For the…
In this paper, we study the propagation of singularities (in the sense of $\mathcal{C}^{\infty}$ wave front set) of the solution of a model case initial-boundary value problem with glancing rays for a concave domain on an asymptotically…
The weak solution to the Navier-Stokes equations in a bounded domain $D \subset \mathbb{R}^3$ with a smooth boundary is proved to be unique provided that it satisfies an additional requirement. This solution exists for all $t \geq 0$. In a…
We consider the Dirichlet boundary value problem for nonlinear systems of partial differential equations with p-structure. We choose two representative cases: the "full gradient case", corresponding to a p-Laplacian, and the "symmetric…
This paper provides a quantitative study of nonnegative solutions to nonlinear diffusion equations of porous medium-type of the form $\partial_t u + {\mathcal L}u^m=0$, $m>1$, where the operator ${\mathcal L}$ belongs to a general class of…
We investigate the existence of positive solutions to the nonlinear second-order three-point integral boundary value problem \begin{equation*} \label{eq-1} \begin{gathered} {u^{\prime \prime}}(t)+f(t, u(t))=0,\ 0<t<T, \\…
We consider the equation $\Delta u=Vu$ in exterior domains in $\mathbb{R}^2$ and $\mathbb{R}^3$, where $V$ has certain periodicity properties. In particular we show that such equations cannot have non-trivial superexponentially decaying…
As an application of the theory of linear parabolic differential equations on noncompact Riemannian manifolds, developed in earlier papers, we prove a maximal regularity theorem for nonuniformly parabolic boundary value problems in…
We study the geometry of domains in complete metric measure spaces equipped with a doubling measure supporting a $1$-Poincar\'e inequality. We propose a notion of \emph{domain with boundary of positive mean curvature} and prove that, for…