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

Previous Page 33 Next

Displaying 641 – 660 of 1411

Showing per page

Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates.

José A. Carrillo, Robert J. McCann, Cédric Villani (2003)

Revista Matemática Iberoamericana

The long-time asymptotics of certain nonlinear , nonlocal, diffusive equations with a gradient flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and Pulvirenti [4] guaranteeing eventual relaxation to equilibrium velocities in a spatially homogencous model of granular flow is extended and quantified by computing explicit relaxation rates. Our arguments rely on establishing generalizations of logarithmic Sobolev inequalities and mass transportation inequalities,...

Klein-Gordon type decay rates for wave equations with time-dependent coefficients

Michael Reissig, Karen Yagdjian (2000)

Banach Center Publications

This work is concerned with the proof of L p - L q decay estimates for solutions of the Cauchy problem for the Klein-Gordon type equation u t t - λ 2 ( t ) b 2 ( t ) ( Δ u - m 2 u ) = 0 . The coefficient consists of an increasing smooth function λ and an oscillating smooth and bounded function b which are uniformly separated from zero. Moreover, m 2 is a positive constant. We study under which assumptions for λ and b one can expect as an essential part of the decay rate the classical Klein-Gordon decay rate n/2(1/p-1/q).

L p -decay of solutions to dissipative-dispersive perturbations of conservation laws

Grzegorz Karch (1997)

Annales Polonici Mathematici

We study the decay in time of the spatial L p -norm (1 ≤ p ≤ ∞) of solutions to parabolic conservation laws with dispersive and dissipative terms added uₜ - uₓₓₜ - νuₓₓ + buₓ = f(u)ₓ or uₜ + uₓₓₓ - νuₓₓ + buₓ = f(u)ₓ, and we show that under general assumptions about the nonlinearity, solutions of the nonlinear equations have the same long time behavior as their linearizations at the zero solution.

L p - L q -Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity

Jerzy Gawinecki (1991)

Annales Polonici Mathematici

We prove the L p - L q -time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the L p - L q -time decay estimates.

Laplace asymptotics for generalized K.P.P. equation

Jean-Philippe Rouquès (2010)

ESAIM: Probability and Statistics

Consider a one dimensional nonlinear reaction-diffusion equation (KPP equation) with non-homogeneous second order term, discontinuous initial condition and small parameter. For points ahead of the Freidlin-KPP front, the solution tends to 0 and we obtain sharp asymptotics (i.e. non logarithmic). Our study follows the work of Ben Arous and Rouault who solved this problem in the homogeneous case. Our proof is probabilistic, and is based on the Feynman-Kac formula and the large deviation principle...

Currently displaying 641 – 660 of 1411