Displaying similar documents to “On the Global Existence of Weak Solutions to A Nonlinear Variational Wave Equation”

Weak solutions to a nonlinear variational wave equation and some related problems

Ping Zhang (2006)

Applications of Mathematics

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In this paper we present some results on the global existence of weak solutions to a nonlinear variational wave equation and some related problems. We first introduce the main tools, the L p Young measure theory and related compactness results, in the first section. Then we use the L p Young measure theory to prove the global existence of dissipative weak solutions to the asymptotic equation of the nonlinear wave equation, and comment on its relation to Camassa-Holm equations in the second...

Multiscale convergence and reiterated homogenization of parabolic problems

Anders Holmbom, Nils Svanstedt, Niklas Wellander (2005)

Applications of Mathematics

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Reiterated homogenization is studied for divergence structure parabolic problems of the form ∂ u ε / ∂ t - div a x , x / ε , x / ε 2 , t , t / ε k ∇ u ε = f . It is shown that under standard assumptions on the function a ( x , y 1 , y 2 , t , τ ) the sequence { u ϵ } of solutions converges weakly in L 2 ( 0 , T ; H 0 1 ( Ω ) ) to the solution u of the homogenized problem ∂ u / ∂ t - div ( b ( x , t ) ∇ u ) = f .

Homogenization of evolution problems for a composite medium with very small and heavy inclusions

Michel Bellieud (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the homogenization of parabolic or hyperbolic equations like ρ ε ∂ n u ε ∂ t n - div ( a ε ∇ u ε ) = f in Ω × ( 0 , T ) + boundary conditions , n ∈ { 1 , 2 } , when the coefficients ρ ε , a ε (defined in Ø ) take possibly high values on a ε -periodic set of grain-like inclusions of vanishing measure. Memory effects arise in the limit problem.