نتایج جستجو برای Variable order diusion and wave equations

تعداد نتایج: 7706980  

Hossein Jafari, Nematollah Kadkhoda, R.M. Ganji,

In this work, we consider variable order difusion and wave equations. The derivative is describedin the Caputo sence of variable order. We use the Genocchi polynomials as basic functions andobtain operational matrices via these polynomials. These matrices and collocation method help usto convert variable order diusion and wave equations to an algebraic system. Some examples aregiven to show the...

2009
Petronela Radu, Borislav Yordanov, BORISLAV YORDANOV,

Abstract. Under appropriate assumptions the energy of wave equations with damping and variable coefficients c(x)utt − div(b(x)∇u) + a(x)ut = h(x, t) has been shown to decay. Determining the decay rate for the higher order energies of the kth order spatial and time derivatives has been an open problem with the exception of some sparse results obtained for k = 1, 2. We establish the sharp gain in...

2006
Steven Paul Levandosky,

may be thought of as a nonlinear beam equation. In this paper we obtain both L-L estimates and space-time integrability estimates on solutions to the linear equation. We also use these estimates to study the local existence and asymptotic behavior of solutions to the nonlinear equation, for nonlinear terms which grow like a certain power of u. The main L-L estimate (Theorem 2.1) states that sol...

2013
NOEL J. WALKINGTON,

The continuous and discontinuous Galerkin time stepping methodologies are combined to develop approximations of second order time derivatives of arbitrary order. This eliminates the doubling of the number of variables that results when a second order problem is written as a first order system. Stability, convergence, and accuracy, of these schemes is established in the context of the wave equat...

2009
JASON METCALFE, DANIEL TATARU,

In this article we consider variable coefficient time dependent wave equations in R×R. Using phase space methods we construct outgoing parametrices and prove Strichartz type estimates globally in time. This is done in the context of C metrics which satisfy a weak asymptotic flatness condition at infinity.

This paper presents discrete Galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. We use the generalized Jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. Numerical results are presented to demonstrate the effectiven...

2009
Sabir Umarov, Stanly Steinberg,

In this paper diffusion processes with changing modes are studied involving the variable order partial differential equations. We prove the existence and uniqueness theorem of a solution of the Cauchy problem for fractional variable order (with respect to the time derivative) pseudo-differential equations. Depending on the parameters of variable order derivatives short or long range memories ma...

2007
GROZDENA TODOROVA, BORISLAV YORDANOV,

We establish weighted L2-estimates for the wave equation with variable damping utt −∆u+ aut = 0 in R, where a(x) ≥ a0(1+ |x|)−α with a0 > 0 and α ∈ [0, 1). In particular, we show that the energy of solutions decays at a polynomial rate t−(n−α)/(2−α)−1 if a(x) ∼ a0|x|−α for large |x|. We derive these results by strengthening significantly the multiplier method. This approach can be adapted to ot...

2008
JASON METCALFE, DANIEL TATARU,

In this article we consider variable coefficient, time dependent wave equations in exterior domains R × (R \ Ω), n ≥ 3. We prove localized energy estimates if Ω is star-shaped, and global in time Strichartz estimates if Ω is strictly convex.

2008
PETRONELA RADU, BORISLAV YORDANOV,

We establish weighted L2−estimates for dissipative wave equations with variable coefficients that exhibit a dissipative term with a space dependent potential. These results yield decay estimates for the energy and the L2−norm of solutions. The proof is based on the multiplier method where multipliers are specially engineered from asymptotic profiles of related parabolic equations.

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