Related papers: On the Classicality of Solutions to a Boundary Val…
In the paper, the contact - boundary value problem with non-classical conditions not requiring agreement conditions is considered for a pseudoparabolic equation. The equivalence of these conditions is substantiated in the case if the…
The aim of this thesis is to derive new gradient estimates for parabolic equations. The gradient estimates found are independent of the regularity of the initial data. This allows us to prove the existence of solutions to problems that have…
We consider the most general class of linear boundary-value problems for higher-order ordinary differential systems whose solutions and right-hand sides belong to the corresponding Sobolev spaces. For parameter-dependent problems from this…
This is the first of a series of papers devoted to the study of classical initial-boundary value problems of Dirichlet, Neumann and mixed type for the Nonlinear Schr\"odinger equation on the segment. Considering proper periodic…
We consider a general inhomogeneous parabolic initial-boundary value problem for a $2b$-parabolic differential equation given in a finite multidimensional cylinder. We investigate the solvability of this problem in some generalized…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
We present a class of non-cylindrical domains where Dirichlet-type problems for parabolic equations, such as the heat equation, can be posed and solved. The regularity for the boundary of this class of domains is a mixed Lipschitz…
We investigate the realization of a myriad of general local and nonlocal inhomogeneous elliptic and parabolic boundary value problems over classes of irregular regions. We present a unified approach in which either local or nonlocal…
We study a family of initial boundary value problems associated to mixed hyperbolic-parabolic systems: v^{\epsilon} _t + A (v^{\epsilon}, \epsilon v^{\epsilon}_x ) v^{\epsilon}_x = \epsilon B (v^{\epsilon} ) v^{\epsilon}_{xx} The…
In this paper we focus on the initial-boundary value problem of the 2-D isentropic Euler equations with damping. We prove the global-in-time existence of classical solution to the initial-boundary value problem by the method of energy…
A class of inverse problems for a heat equation with involution perturbation is considered using four different boundary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence…
The autor considers an initial-boundary value problem for the nonstationary Stokes system in an angle, where Dirichlet and Neumann conditions are prescribed on the diferent sides of the angle. The major part of the paper deals with the…
Hyperbolic systems of the first and higher-order partial differential equations appear in many multiphysics problems. We will be dealing with a wave propagation problem in a piece-wise homogeneous medium. Mathematically, the problem is…
The article considers the Dirichlet problem for a high-order mixed-type equation that splits into factors, each of which is a Lavrentiev-Bitsadze equation with its own excellent coefficient. Sufficient conditions are found for the…
We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…
The standard problem for the classical heat equation posed in a bounded domain $\Omega$ of $\mathbb R^n$ is the initial and boundary value problem. If the Laplace operator is replaced by a version of the fractional Laplacian, the initial…
In 2002, J.M.Rassias (Uniqueness of quasi-regular solutions for bi-parabolic elliptic bi-hyperbolic Tricomi problem, Complex Variables, 47 (8) (2002), 707-718) imposed and investigated the bi-parabolic elliptic bi-hyperbolic mixed type…
We present an algorithm for characterising the generalised Dirichlet to Neumann map for moving initial-boundary value problems. This algorithm is derived by combining the so-called global relation, which couples the initial and boundary…
We consider initial boundary value problems with the homogeneous Neumann boundary condition. Given an initial value, we establish the uniqueness in determining a spatially varying coefficient of zeroth-order term by a single measurement of…
In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Two theorems on strong solvability and the…