Search results for "cauchy problem"

Solution of a cauchy problem for an infinite chain of linear differential equations

2005

Defining the recurrence relations for orthogonal polynomials we have found an exact solution of a Cauchy problem for an infinite chain of linear differential equations with constant coefficients. These solutions have been found both for homogeneous and an inhomogeneous systems.

Stellar hydrodynamics with glaister's riemann solver: An approach to the stellar collapse

1990

La resolution de Remann approximee de la solution des equations d'Euler de la dynamique des gaz 1 D, developpee par Glaister P. (1988, J. Comput. Phys., 74) est introduite dans un code hydrodynamique lagrangien et appliquee a l'effondrement stellaire a symetrie spherique

Regularity of solutions of cauchy problems with smooth cauchy data

1988

The cauchy problem for non-linear Klein-Gordon equations

1993

We consider in ℝ n+1,n≧2, the non-linear Klein-Gordon equation. We prove for such an equation that there is a neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincare covariant then the non-linear representation of the Poincare Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincare group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the …

Systèmes hyperboliques d'équations aux dérivées partielles linéaires : régularité et matrices diagonalisables

2001

Resume La regularite des solutions d'un systeme d'equations aux derivees partielles hyperbolique, est liee aux proprietes spectrales d'un faisceaux de matrices reelles. Nous nous interessons ici a la regularite L 2 . Celle ci est obtenue si et seulement si l'exponentielle imaginaire du faisceau est bornee. Nous regardons le lien entre cette condition et les proprietes spectrales du faisceau, ici diagonalisable sur R . Nous donnons en particulier un critere d'exponentielle bornee si les valeurs propres ne sont pas de multiplicites constantes, et nous montrons que dans le cas des faisceaux engendres par deux matrices 3×3, l'exponentielle est bornee si et seulement si le faisceau est analytiqu…

Existence results and asymptotic behavior for nonlocal abstract Cauchy problems

2008

AbstractThe purpose of this paper is to study the existence and asymptotic behavior of solutions for Cauchy problems with nonlocal initial datum generated by accretive operators in Banach spaces.

Exact treatment of linear difference equations with noncommutative coefficients

2007

The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.

Exact treatment of operator difference equations with nonconstant and noncommutative coefficients

2013

We study a homogeneous linear second-order difference equation with nonconstant and noncommuting operator coefficients in a vector space. We build its exact resolutive formula consisting of the explicit noniterative expression of a generic term of the unknown sequence of vectors. Some nontrivial applications are reported in order to show the usefulness and the broad applicability of the result.

Fully reliable a posteriori error control for evolutionary problems

2015

Existence and Regularity for a Class of Nonlinear Hyperbolic Boundary Value Problems

2002

AbstractThe regularity of the solution of the telegraph system with nonlinear monotone boundary conditions is investigated by two methods. The first one is based on D'Alembert-type representation formulae for the solution. In the second method the telegraph system is reduced to a linear Cauchy problem with a locally Lipschitzian functional perturbation; then regularity results are established by appealing to the theory of linear semigroups.