Related papers: A Boundary Value Problem for a Class of Anisotropi…
We consider a mixed type boundary value problem for a class of degenerate parabolic-hyperbolic equations. Namely, we consider a Cartesian product domain and split its boundary into two parts. In one of them we impose a Dirichlet boundary…
We study a Neumann type initial-boundary value problem for strongly degenerate parabolic-hyperbolic equations under the nonlinearity-diffusivity condition. We suggest a notion of entropy solution for this problem and prove its uniqueness.…
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 deal with a linear hyperbolic differential operator of the second order on a bounded planar domain with a smooth boundary. We establish a well-posedness result in case where a mixed, Dirichlet-Neumann, condition is prescribed on the…
We study a parabolic initial-boundary-value problem for a system of two differential equations with two boundary conditions of different orders, the Dirichlet and Neumann ones. It occurs specifically in the heat-mass transfer theory. We…
In this paper, we are concerned with the first initial boundary value problem for a class of fully nonlinear parabolic equations on Riemannian manifolds. As usual, the establishment of the a priori C^2 estimates is our main part. Based on…
This paper is concerned with the initial boundary value problem for a nonconservative system of hyperbolic equation appearing in elastodynamics in the space time domain $x > 0, t > 0$. The number of boundary conditions to be prescribed at…
In present paper we study a boundary value problem for a mixed parabolic-hyperbolic type equation in a rectangular domain and prove the existence of unique solution of this problem. In theory of boundary value problems for second order…
In this paper we consider an initial boundary value problem for a semilinear parabolic equation with nonlinear nonlocal boundary condition. We prove comparison principle, the existence theorem of a local solution and study the problem of…
In this paper we establish weighted $L^{q}$-$L^{p}$-maximal regularity for linear vector-valued parabolic initial-boundary value problems with inhomogeneous boundary conditions of static type. The weights we consider are power weights in…
Here a mixed problem for a nonlinear hyperbolic equation with Neumann boundary value condition is investigated, and a priori estimations for the possible solutions of the considered problem are obtained. These results demonstrate that any…
In this paper we consider an initial boundary value problem for a semilinear parabolic equation with absorption and nonlinear nonlocal Neumann boundary condition. We prove comparison principle, the existence theorem of a local solution and…
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…
End-point maximal $L^1$-regularity for parabolic initial-boundary value problems is considered. For the inhomogeneous Dirichlet and Neumann data, maximal $L^1$-regularity for initial-boundary value problems is established in time end-point…
This paper discusses the initial-boundary value problem (with a nonhomogeneous boundary condition) for a multi-dimensional scalar first-order conservation law with a multiplicative noise. One introduces a notion of kinetic formulations in…
We investigate a general nonhomogeneous parabolic initial-boundary value problem in some anisotropic H\"ormander inner product spaces. We prove that the operators corresponding to this problem are isomorphisms between appropriate…
In this paper we are concerned with the initial boundary value problems of linear and semi-linear parabolic equations with mixed boundary conditions on non-cylindrical domains in spatial-temporal space. We obtain the existence of a weak…
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…
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 prove new existence and uniqueness results for weak solutions to non-homogeneous initial-boundary value problems for parabolic equations modeled on the evolution of the p-Laplacian.