Related papers: Cubic String Boundary Value Problems and Cauchy Bi…
We consider operator-valued boundary value problems in $(0,2\pi)^n$ with periodic or, more generally, $\nu$-periodic boundary conditions. Using the concept of discrete vector-valued Fourier multipliers, we give equivalent conditions for the…
This course is intended as an introduction to the analysis of elliptic partial differential equations. The objective is to provide a large overview of the different aspects of elliptic partial differential equations and their modern…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the equation can be degenerate. Some generalized solutions…
The dynamical boundary value problem for viscoelastic half-space with cut in the form of a strip is considered. The problem is reduced to the singular integral equation of first kind. Using the method of orthogonal polynomials, the integral…
In this paper we consider a class of isospectral deformations of the inhomogeneous string boundary value problem. The deformations considered are generalizations of the isospectral deformation that has arisen in connection with the…
In this article, the authors survey and review the studies of boundary value problems for regular functions in Clifford analysis, which include theoretical foundations and useful methods. Its theoretical bases consist of the generalized…
We consider the hermitian random matrix model with external source and general polynomial potential, when the source has two distinct eigenvalues but is otherwise arbitrary. All such models studied so far have a common feature: an…
In a multidimensional infinite layer bounded by two hyperplanes, the Poisson equation with the polynomial right-hand side is considered. It is shown that the Dirichlet boundary value problem and the mixed Dirichlet-Neumann boundary value…
Initial-boundary value problems on a half-strip with different types of boundary conditions for the generalized Kawahara-Zakharov-Kuznetsov equation with nonlinearity of higher order are considered. In particular, nonlinearity can be…
The classical approach to diffusion processes is based on Fick's law that the flux is proportional to the concentration gradient. Various phenomena occurring during propagation of penetrating liquids in polymers show that this type of…
The Degasperis--Procesi (DP) equation can be viewed as an isospectral deformation of the boundary value problem for the so-called cubic string, while the Novikov equation can be formally regarded as linked to the dual cubic string. However,…
We study quasi-periodic eigenvalue problems that arise in the stability analysis of periodic traveling wave solutions to Hamiltonian PDEs. We establish bounds on regions in the complex plane when the eigenvalues may deviate from the…
We consider existence of periodic boundary value problems of nonlinear second order ordinary differential equations. Under certain half Lipschitzian type conditions several existence results are obtained. As applications positive periodic…
We consider the Cauchy problem for a second order quasi-linear partial differential equation with an admissible parabolic degeneration such that the given functions described the initial conditions are defined on a closed interval. We study…
Sixth-order boundary value problems (BVPs) arise in thin-film flows with a surface that has elastic bending resistance. To solve such problems, we first derive a complete set of odd and even orthonormal eigenfunctions -- resembling…
We prove that both local and non-local formulations of the Degasperis-Procesi equation possess a pseudospherical nature. As a result, solutions determined by Cauchy problems with non-trivial initial data and a minimal specific regularity…
Initial-boundary value problems in a half-strip with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global existence, uniqueness and long-time decay of weak and regular…
Parabolic integro-differential nondegenerate Cauchy problem is considered in the scale of L_{p} spaces of functions whose regularity is defined by a Levy measure with O-regulary varying radial profile. Existence and uniqueness of a solution…
We study some functionals associated with a process driven by a fractional boundary value problem (FBVP for short). By FBVP we mean a Cauchy problem with boundary condition written in terms of a fractional equation, that is an equation…