Related papers: Initial boundary value problem for a semilinear pa…
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…
This paper investigates the initial boundary value problem for a fractional pseudo-parabolic equation with singular potential. The global existence and blow-up of solutions to the initial boundary value problem are obtained at low initial…
We consider one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. Results on $C^m$-regularity of the free boundary are obtained. In particular, a necessary and…
We establish the well-posedness of an initial-boundary value problem of mixed type for a stochastic nonlinear parabolic-hyperbolic equation on a space domain $\cO=\cO'\X\cO''$ where a Neumann boundary condition is imposed on…
The initial-boundary value problems for linear non-autonomous first order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change…
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…
This paper deals with the initial-boundary value problem to a nonlocal semilinear pseudo-parabolic equation with conical degeneration, which has been studied in [Global well-posedness for a nonlocal semilinear pseudo-parabolic equation with…
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…
Evolution PDEs for dispersive waves are considered in both linear and nonlinear integrable cases, and initial-boundary value problems associated with them are formulated in spectral space. A method of solution is presented, which is based…
An initial-value problem for an ordinary differential equation of the first order, is considered. It is supposed that the right-hand side of the equation is a continuous function defined on a set consisting of an open set and a part of its…
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 prove, by adapting the method of Colliander-Kenig (2002), local well-posedness of the initial-boundary value problem for the one-dimensional nonlinear Schroedinger equation on the half-line under low boundary regularity assumptions.
The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the…
In this paper, we consider a semilinear parabolic equation with nonlinear nonlocal Neumann boundary condition and nonnegative initial datum. We first prove global existence results. We then give some criteria on this problem which determine…
We prove the global classical solvability of initial-boundary problems for semilinear first-order hyperbolic systems subjected to local and nonlocal nonlinear boundary conditions. We also establish lower bounds for the order of nonlinearity…
In this paper, we consider the initial boundary value problem for a pseudo-parabolic Kirchhoff equation with logarithmic nonlinearity. We use the potential well method to give a threshold result of global existence and finite-time blow-up…
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…
While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…
We study a class of initial boundary value problems of hyperbolic type. A new topological approach is applied to prove the existence of non-negative classical solutions. The arguments are based upon a recent theoretical result.
We analyze the initial value problem for semilinear wave equations on asymptotically anti-de Sitter spaces using energy methods adapted to the geometry of the problem at infinity. The key feature is that the coefficients become strongly…