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Time splitting for wave equations in random media
Time splitting wave equations random media
2015/7/14
Numerical simulation of high frequency waves in highly heterogeneous media is a challenging problem. Resolving the fine structure of the wave field typically requires extremely small time steps and sp...
Random Attractors for Stochastic Wave Equations with Critical Exponents on Rn
Stochastic Wave Equations Random Attractors
2015/4/3
Outline
• Stochastic wave equations on Rn.
• Random attractors theory.
• Random absorbing sets for wave equations.
• Pullback asymptotic compactness.
• Existence of ...
New Bilinear Estimates for Quadratic-Derivative Nonlinear Wave Equations in 2+1 Dimensions
Bilinear Estimates Quadratic-Derivative Nonlinear
2014/12/8
This thesis is concerned with the Cauchy problem for the quadratic derivative nonlinear wave equation in two spatial dimensions. Using standard techniques, we reduce local well-posedness in Fourier Le...
A LARGE DATA REGIME FOR NON-LINEAR WAVE EQUATIONS
A LARGE DATA REGIME NON-LINEAR WAVE EQUATIONS
2018/4/19
For semi-linear wave equations with null form non-linearities on R3+1, we exhibit an open set of initial data which are allowed to be large in energy spaces, yet we can still obtain global solutions i...
On Control Of Sobolev Norms For Some Semilinear Wave Equations With Localized Data
Control Sobolev Norms Some Semilinear Wave Equations Localized Data
2012/4/16
We establish new bounds of the Sobolev norms of solutions of semilinear wave equations for data lying in the Hs, s<1, closure of compactly supported data inside a ball of radius R, with R a fixed and ...
Quasi-periodic Solutions for 2k Order Wave Equations
2k order wave equations KAM theory Quasi-periodic solutions Partial Birkhoff normal form
2011/10/18
In this paper, we consider one-dimensional (1D) nonlinear 2k order wave equations under the Dirichlet boundary conditions, weher the nonlinearity f is an analytic, odd function. It is proved that for ...
Averaging approximation to singularly perturbed nonlinear stochastic wave equations
stochastic nonlinear wave equations averaging tightness martingale
2011/9/16
Abstract: An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on...
Dimension of attractors and invariant sets of damped wave equations in unbounded domains
damped wave equation invariant set attractor dimension
2011/9/5
Abstract: Under fairly general assumptions, we prove that every compact invariant set $\mathcal I$ of the semiflow generated by the semilinear damped wave equation u_{tt}+\alpha u_t+\beta(x)u-\Deltau ...
Wave equations on non-smooth space-times
Wave equation, Cauchy problem, global hyperbolicity, distributional solutions, generalized solutions
2011/8/22
Abstract: We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distr...
Strichartz estimates for Dirichlet-wave equations in two dimensions with applications
Strichartz estimtes Strauss conjecture obstacles
2011/2/21
We establish the Strauss conjecture for nontrapping obstacles when the spatial dimension n is two. As pointed out in [7] this case is more subtle than n = 3 or 4 due to the fact that the arguments of ...
Multiplicity and regularity of periodic solutions for a class of degenerate semilinear wave equations
Multiplicity regularity of periodic solutions class of degenerate semilinear wave equations
2011/2/28
We prove the existence of infinitely many classical periodic solutions for a class of degenerate semilinear wave equations:utt − uxx + |u|s−1u = f(x, t),for all s > 1. In particular we pro...
Differential transform solution of some linear wave equations with mixed nonlinear boundary conditions and its blow up
Wave Equation Series Solution Energy Equation, Blow up
2010/9/20
Using Differential Transform to solve blow up solutions of some linear wave equation with mixed non-linear boundary conditions is proposed in this study.Non-linear boundary conditions cause the finite...
Abstract Wave Equations and Associated Dirac-Type Operators
Dirac operators supersymmetry wave equations semigroups
2011/2/25
We discuss the unitary equivalence of generators GA,R associated with abstract damped wave equations of the type u¨+Ru˙ +AAu = 0 in some Hilbert space H1 and certain non-self-adjoint Dirac-type opera...
Reduction of Multidimensional Wave Equations to Two-Dimensional Equations: Investigation of Possible Reduced Equations
Mathematical Physics (math-ph) Analysis of PDEs (math.AP) Exactly Solvable and Integrable Systems (nlin.SI)
2010/11/11
We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigati...
The Null Condition and Global Existence for Nonlinear Wave Equations on Slowly Rotating Kerr Spacetimes
Null Condition Global Existence Nonlinear Wave Equations Rotating Kerr Spacetimes
2010/12/16
We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in tim...