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Existence Theorems for the Dirichlet Elliptic Inclusion Involving Exponential-Growth-Type Multivalued Right-Hand Side

Hôǹg Thái Nguyêñ, Dariusz Pączka (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

We present two existence results for the Dirichlet elliptic inclusion with an upper semicontinuous multivalued right-hand side in exponential-type Orlicz spaces involving a vector Laplacian, subject to Dirichlet boundary conditions on a domain Ω⊂ ℝ². The first result is obtained via the multivalued version of the Leray-Schauder principle together with the Nakano-Dieudonné sequential weak compactness criterion. The second result is obtained by using the nonsmooth variational technique together with...

Explicit difference schemes for nonlinear differential functional parabolic equations with time dependent coefficients-convergence analysis

A. Poliński (2006)

Annales Polonici Mathematici

We study the initial-value problem for parabolic equations with time dependent coefficients and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyze convergence of explicit finite difference schemes by means of discrete fundamental solutions.

Exponential convergence to the stationary measure and hyperbolicity of the minimisers for random Lagrangian Systems

Boritchev, Alexandre (2017)

Proceedings of Equadiff 14

We consider a class of 1d Lagrangian systems with random forcing in the spaceperiodic setting: φ t + φ x 2 / 2 = F ω , x S 1 = / . These systems have been studied since the 1990s by Khanin, Sinai and their collaborators [7, 9, 11, 12, 15]. Here we give an overview of their results and then we expose our recent proof of the exponential convergence to the stationary measure [6]. This is the first such result in a classical setting, i.e. in the dual-Lipschitz metric with respect to the Lebesgue space L p for finite p , partially answering...

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