All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 28

Showing per page

Cauchy problem for a class of parabolic systems of Shilov type with variable coefficients

Vladyslav Litovchenko, Iryna Dovzhytska (2012)

Open Mathematics

In the case of initial data belonging to a wide class of functions including distributions of Gelfand-Shilov type we establish the correct solvability of the Cauchy problem for a new class of Shilov parabolic systems of equations with partial derivatives with bounded smooth variable lower coefficients and nonnegative genus. We also investigate the conditions of local improvement of the convergence of a solution of this problem to its limiting value when the time variable tends to zero.

Coherent nonlinear waves and the Wiener algebra

Guy Métivier, Jean-Luc Joly, Jeffrey Rauch (1994)

Annales de l'institut Fourier

We study oscillatory solutions of semilinear first order symmetric hyperbolic system L u = f ( t , x , u , u ‾ ) , with real analytic f .The main advance in this paper is that it treats multidimensional problems with profiles that are almost periodic in T , X with only the natural hypothesis of coherence.In the special case where L has constant coefficients and the phases are linear, the solutions have asymptotic description u ϵ = U ( t , x , t / ϵ , x / ϵ ) + o ( 1 ) where the profile U ( t , x , T , X ) is almost periodic in ( T , X ) .The main novelty in the analysis is the space of profiles which...

Continuity of the quenching time in a semilinear parabolic equation

Théodore Boni, Firmin N'Gohisse (2008)

Annales UMCS, Mathematica

In this paper, we consider the following initial-boundary value problem [...] where Ω is a bounded domain in RN with smooth boundary ∂Ω, p > 0, Δ is the Laplacian, v is the exterior normal unit vector on ∂Ω. Under some assumptions, we show that the solution of the above problem quenches in a finite time and estimate its quenching time. We also prove the continuity of the quenching time as a function of the initial data u0. Finally, we give some numerical results to illustrate our analysis.

Continuous dependence estimates for the ergodic problem of Bellman-Isaacs operators via the parabolic Cauchy problem

Claudio Marchi (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This paper concerns continuous dependence estimates for Hamilton-Jacobi-Bellman-Isaacs operators. We establish such an estimate for the parabolic Cauchy problem in the whole space  [0, +∞) × ℝn and, under some periodicity and either ellipticity or controllability assumptions, we deduce a similar estimate for the ergodic constant associated to the operator. An interesting byproduct of the latter result will be the local uniform convergence for some classes of singular perturbation problems.

Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies

Ken Shirakawa (2009)

Banach Center Publications

In this paper, a one-dimensional Euler-Lagrange equation associated with the total variation energy, and Euler-Lagrange equations generated by approximating total variations with linear growth, are considered. Each of the problems presented can be regarded as a governing equation for steady-states in solid-liquid phase transitions. On the basis of precise structural analysis for the solutions, the continuous dependence between the solution classes of approximating problems and that of the limiting...

Continuous dependence of the entropy solution of general parabolic equation

Mohamed Maliki (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

We consider the general parabolic equation : u t - Δ b ( u ) + d i v F ( u ) = f in Q = ] 0 , T [ × ℝ N , T > 0 with u 0 ∈ L ∞ ( ℝ N ) , for a ....

Currently displaying 1 – 20 of 28

Page 1 Next