Related papers: Dirichlet boundary valued problems for linear and …
Evolution of weakly nonlinear and slowly varying Rossby waves in planetary atmospheres and oceans is considered within the quasi-geostrophic equation on unbounded domains. When the mean flow profile has a jump in the ambient potential…
In this paper, we study the full regularity and well-posedness of classical solutions to the nonlinear unsteady Prandtl equations with Robin or Dirichlet boundary condition in half space. Under Oleinik's monotonicity assumption, we prove…
In this paper we introduce new characterizations of spectral fractional Laplacian to incorporate nonhomogeneous Dirichlet and Neumann boundary conditions. The classical cases with homogeneous boundary conditions arise as a special case. We…
We prove that the time-harmonic solutions to Maxwell's equations in a 3D exterior domain converge to a certain static solution as the frequency tends to zero. We work in weighted Sobolev spaces and construct new compactly supported…
We consider the Poisson equation with homogeneous Dirichlet conditions in a family of domains in $R^{n}$ indexed by a small parameter $\epsilon$. The domains depend on $\epsilon$ only within a ball of radius proportional to $\epsilon$ and,…
We consider approximating the solution of the Helmholtz exterior Dirichlet problem for a nontrapping obstacle, with boundary data coming from plane-wave incidence, by the solution of the corresponding boundary value problem where the…
This article provides a new approach to address Mosco convergence of gradient-type Dirichlet forms, $\mathcal E^N$ on $L^2(E,\mu_N)$ for $N\in\mathbb N$, in the framework of converging Hilbert spaces by K.~Kuwae and T.~Shioya. The basic…
For $2a$-order strongly elliptic operators $P$ generalizing $(-\Delta )^a$, $0<a<1$, the treatment of the homogeneous Dirichlet problem on a bounded open set $\Omega \subset R^n$ by pseudodifferential methods, has been extended in a recent…
We consider an initial mixed-boundary value problem for anisotropic fractional type degenerate parabolic equations posed in bounded domains. Namely, we consider that the boundary of the domain splits into two parts. In one of them, we…
We consider a flow of non-Newtonian heat conducting incompressible fluid in a bounded domain subjected to the homogeneous Dirichlet boundary condition for the velocity field and the spatially inhomogeneous Dirichlet boundary condition for…
We investigate sufficient H\"older continuity conditions on Leray-Hopf (weak) solutions to the in unsteady Navier-Stokes equations in three dimensions guaranteeing energy conservation. Our focus is on the half-space case with homogeneous…
We study the defocusing semilinear wave equation in ${\mathbb{R}}\times{\mathbb{R}}^2\backslash{\mathcal K}$ with the Dirichlet boundary condition, where ${\mathcal K}$ is a star-shaped obstacle with smooth boundary. We first show that the…
In this paper, we study the one-dimensional wave equation with localized nonlinear damping and Dirichlet boundary conditions, in the $L^p$ framework, with $p\in [1,\infty)$. We start by addressing the well-posedness problem. We prove the…
In a multidimensional infinite layer bounded by two hyperplanes, the inhomogeneous Helmholtz equation with a polynomial right-hand side is considered. It is shown that the Dirichlet and Dirichlet-Neumann boundary-value problems with…
This work contributes to an understanding of the domain size's effect on the existence and uniqueness of the linear convection--diffusion equation with integral-type boundary conditions, where boundary conditions depend non-locally on…
We establish a mixed observability inequality for a class of degenerate hyperbolic equations on the cylindrical domain $\Omega = \mathbb{T} \times (0,1)$ with mixed Neumann Dirichlet boundary conditions. The degeneracy acts only in the…
In this article, first we give a general lemma on the existence of regular homeomorphic solutions $f$ with the hydrodynamic normalization $f(z)=z+o(1)$ as $z\to\infty$ to the degenerate Beltrami equations $\overline{\partial}f=\mu\,\partial…
In this paper, we consider the initial boundary value problem of a doubly nonlinear parabolic equation with nonlinear perturbation. We impose the homogeneous Dirichlet condition on this problem. We aim to reduce the growth condition of the…
We are concerned with the study of the existence and multiplicity of solutions for Dirichlet boundary value problems, involving the $( p( m ), \, q( m ) )-$ equation and the nonlinearity is superlinear but does not fulfil the…
This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…