Related papers: A generalized initial value problem for ODE's

Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…

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…

In the present paper, several properties concerning generalized derivatives of multifunctions implicitly defined by set-valued inclusions are studied by techniques of variational analysis. Set-valued inclusions are problems formalizing the…

We consider an initial value problem for time-fractional evolution equation in Banach space $X$: $$ \pppa (u(t)-a) = Au(t) + F(t), \quad 0<t<T. \eqno{(*)} $$ Here $u: (0,T) \rrrr X$ is an $X$-valued function defined in $(0,T)$, and $a \in…

We characterize generalized derivatives of the solution operator of the obstacle problem. This precise characterization requires the usage of the theory of so-called capacitary measures and the associated solution operators of relaxed…

This paper investigates new first-order optimality conditions for general optimization problems. These optimality conditions are stronger than the commonly used M-stationarity conditions and are in particular useful when the latter cannot…

We give a short proof of local well-posedness for the initial boundary value problem in general relativity with sole boundary condition the requirement that the boundary is umbilic. This includes as a special case the totally geodesic…

We discuss first order systems of rational difference equations which have the property that lines through the origin are mapped into lines through the origin. We call such systems projective systems of rational difference equations and we…

Global smooth solutions to the initial value problem for systems of nonlinear wave equations with multiple propagation speeds will be constructed in the case of small initial data and nonlinearities satisfying the null condition.

Initial-boundary value problems in a bounded rectangle with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in the classes of weak and regular solution…

Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background…

We consider an inhomogeneous initial-boundary value problem for a Petrovskii parabolic system of second order PDEs. We prove that this problem induces isomorphisms between appropriate anisotropic generalized Sobolev spaces. The regularity…

We are interested in the relative conditioning of the problem $y_0\mapsto \mathrm{e}^{tA}y_0$, i.e., the relative conditioning of the action of the matrix exponential $\mathrm{e}% ^{tA}$ on a vector with respect to perturbations of this…

A new method for the optimal solutions is proposed. Originating from the continuous-time dynamics stability theory in the control field, the optimal solution is anticipated to be obtained in an asymptotically evolving way. By introducing a…

In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…

When one wishes to numerically solve an initial value problem, it is customary to rewrite it as an equivalent first-order system to which a method, usually from the class of Runge-Kutta methods, is applied. Directly treating higher-order…

A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system…

We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…

Chen and Hsiao gave the numerical solution of initial value problems of systems of linear differential equations with constant coefficients by Walsh polynomials approach. This result was improved by G\'at and Toledo for initial value…

The late-time phase-ordering kinetics of the O(n) model for a non-conserved order parameter are considered for the case where the O(n) symmetry is broken by the initial conditions or by an external field. An approximate theoretical…