Related papers: Classical solvability of nonlinear initial-boundar…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
We consider a hyperbolic ordinary differential equation perturbed by a nonlinearity which can be singular at a point and in particular this includes MEMS type equations. We first study qualitative properties of the solution to the…
We consider an initial value problem for a nonlinear parabolic equation with memory under nonlinear nonlocal boundary condition. In this paper we study classical solutions. We establish the existence of a local maximal solution. It is shown…
The classical solvability of the initial-boundary problem for the Davey-Stewartson-II type system of equations is proved.
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…
In this paper we establish the theory on semiglobal classical solution to first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions, and based on this, the corresponding exact boundary controllability and…
We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic…
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…
We prove well posedness and stability in $\mathbf{L}^1$ for a class of mixed hyperbolic-parabolic non linear and non local equations in a bounded domain with no flow along the boundary. While the treatment of boundary conditions for the…
We obtain an upper bound on the initial blow-up of nonnegative solutions of second order semilinear parabolic inequalities when a superlinear exponent in the inequalities is not too large.
We investigate global bounded solutions of higher regularity to boundary value problems for a general linear nonautonomous first order 1D hyperbolic system in a strip. We establish the existence of such solutions under the assumption of…
The behavior of sufficiently regular solutions to semilinear hyperbolic equations has attracted a great deal of attention in the past decades, concerning local/global existence, finite time blow-up, critical exponents, and propagation of…
For a certain class of genuinely nonlinear two-by-two planar hyperbolic systems we show that any classical solution on a smoothly bounded domain has nontangential boundary limits except on a set whose Hausdorff dimension is bounded by some…
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…
In this article, we consider fully nonlinear, possibly degenerate, parabolic equations associated with Ventcell boundary conditions in bounded or unbounded, smooth domains. We first analyze the exact form of such boundary conditions in…
We investigate the finite time stability property of one-dimensional nonautonomous initial boundary value problems for linear decoupled hyperbolic systems with nonlinear boundary conditions. We establish sufficient and necessary conditions…
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 initial boundary value problem for a parabolic equation with nonlinear memory and absorption under nonlinear nonlocal boundary condition. We prove global existence and blow-up of solutions.
For regular and nonregular (singular) semilinear differential-algebraic equations (DAEs), we prove theorems on the existence and uniqueness of global solutions and on the blow-up of solutions, which allow one to identify the sets of initial…
Bernoulli's free boundary problem is an overdetermined problem in which one seeks an annular domain such that the capacitary potential satisfies an extra boundary condition. There exist two different types of solutions called elliptic and…