schrödinger equation for the harmonic oscillator the hermite equation

... 1.1 The equations in 1.1 describe the macroscopic behavior of the magnetohydrodynamic flow This is a three-dimensional magnetohydrodynamic flow which is uniform in the transverse directions There ... of 1.1 , namely, we consider the magnetohydrodynamic equations for isentropic compressible fluids Thus, instead of the equations in 1.1 , we will study the following equations: ρt ρu ρu2 t ρw bt ... Assume also that the following compatibility conditions hold for the initial data: b0 γ λu0xx − Rρ0 μw0xx ρ1/2 f x ρ1/2 g b0x for some f ∈ L2 Ω , 1.9 for some g ∈ L2 Ω 1.10 Then there exists a...

Ngày tải lên: 22/06/2014, 06:20

... 1.1 The equations in 1.1 describe the macroscopic behavior of the magnetohydrodynamic flow This is a three-dimensional magnetohydrodynamic flow which is uniform in the transverse directions There ... of 1.1 , namely, we consider the magnetohydrodynamic equations for isentropic compressible fluids Thus, instead of the equations in 1.1 , we will study the following equations: ρt ρu ρu2 t ρw bt ... Assume also that the following compatibility conditions hold for the initial data: b0 γ λu0xx − Rρ0 μw0xx ρ1/2 f x ρ1/2 g b0x for some f ∈ L2 Ω , 1.9 for some g ∈ L2 Ω 1.10 Then there exists a...

Ngày tải lên: 22/06/2014, 19:20

... of the A -harmonic equation and the obstacle problems for differential forms which satisfy the A -harmonic equation, and the proof for the uniqueness of the solution to the obstacle problem of the ... relations between the solution to Aharmonic equation and the solution to obstacle problem of A -harmonic equation We have the following two theorems Theorem 2.6 If a differential form u is a supersolution ... research on the obstacle problem for differential forms satisfying the A -harmonic equation and we hope that our work will stimulate further research in this direction By the some definitions as the solution,...

Ngày tải lên: 21/06/2014, 18:20

... In the third section, we will give a geometrical link for the best discretization of the harmonic oscillator equation In the fourth section, we treat the existence and uniqueness problem for ... difference equations, but additional difficulties appear, because among other things, we need to get explicit formulas for the solution of the equation to be studied We study in this paper the discrete ... Advances in Difference Equations where Δ denotes the forward difference operator of the first order, that is, for each x : Z → X, and n ∈ Z , Δxn xn − xn On the other hand, in the article , a characterization...

Ngày tải lên: 22/06/2014, 11:20

... the weakly damped harmonic oscillator equation (ω0 = 1, γ = 0.1) for large t and ε = 0.2 The comparison of the exact discretization (6.13) with three other discrete equations simulating the harmonic ... representing the equation in the form of a matrix equation of the first order The general linear discrete equation of the second order, xn+2 = 2Axn+1 + Bxn , (A.1) can be rewritten in the matrix form ... Simulations of the harmonic oscillator equation The general solution of (A.2) has, obviously, the following form: yn = M n y0 , (A.4) and the solution of a difference equation is reduced to the purely...

Ngày tải lên: 22/06/2014, 22:20

... this all together, we obtain O(vlo ∇vhi ) −1/2 −δ ε1/2−δ N1 min(N4 , εN4 1/2 6/5 L2 Lx t ) N1 ≥N2 ≥N3 ≥N4 Performing the N1 sum, then the N2 , then the N3 , then the N4 , we obtain the desired ... from the rest of the solution One then removes this bubble, the remainder of the solution evolves, and then one uses perturbation theory, augmented with the additional information about the isolation ... (4.12) which completes the proof of Theorem 1.1 The proofs of the above claims occupy the remainder of this paper Before moving to these proofs, we summarize the role of the parameters ηi , i...

Ngày tải lên: 16/02/2014, 06:20

... and reduce the dispersive estimates to their dyadic counterparts Section contains the construction of a parametrix for the linear equation We start by using the information we have for the characteristic ... RESULTS FOR THE NONLINEAR WAVE EQUATION Hence the contraction principle implies that we may write the solution v in the form v = v + TF , ˜ where v is the approximate solution formed above for data ... represent solutions to the linear equation is inspired by the work of Smith [23], but the ansatz for the development of such packets, as well as the orthogonality arguments for them, is considerably...

Ngày tải lên: 15/03/2014, 09:20

... the b-wave front set based on H (X) there The following section is devoted to the elliptic estimates for the wave equation These are obtained from the microlocal positivity of the Dirichlet form, ... all in this proof The novelty is thus the use of the Dirichlet form (hence the H -based wave front set) for the proof of both the elliptic and hyperbolic/glancing estimates, and the systematic use ... Melrose for his interest in this project, for reading, and thereby improving, parts of the paper, and for numerous helpful and stimulating discussions, especially for the wave equation on forms...

Ngày tải lên: 15/03/2014, 09:20

Ngày tải lên: 17/03/2014, 14:41

Ngày tải lên: 24/04/2014, 17:25

... data for the Burgers equation (1) The Neumann problem on the semi-line for υ(x,t) is then in principle solved through the following prescription: Solve the Neumann problem on the semi-line for ... on the use of the contraction-mapping technique, analogously to what was done for the Eckhaus equation in [15] In particular, the main result of the present study is to prove the following Theorem ... technique for solving a nonlinear integro-differential equation like (11) On the other hand, the determination of the solution u(x,t) has been reduced to the solution of the nonlinear integral equation...

Ngày tải lên: 20/06/2014, 22:20

... σj (Q) = σj (Q) for j = 1, 2, 3, then Q(x) = Q(x) on [0, π] The purpose of this paper is to generalize the above theorem for the case m ≥ The idea we use is the Weyl’s matrix for matrix-valued ... shall prove the first main theorem For simplicity, if a symbol a denotes an object related to Lm(Q, h, H), then the symbol α denotes the analogous object related ˜ ˜ H) to Lm (Q, h, Theorem 2.3 ... (λ) = ij (λ) for ≤ i < j ≤ m ˜ ˜ ˜ This implies Lm (Q, h, H) = Lm (Q, h, H) The authors want to emphasis that for n = 1, the result is classical; for n = 2, Theorem 2.6 leads to Theorem 1.1 Shen...

Ngày tải lên: 20/06/2014, 22:20

... generalization of the moving boundary problem for the classical heat equation [13] which can be useful in the study of free boundary problems for the heat-diffusion equation [12] We will use the Neumann ... the form (6.7), then the functions V, j1 and j2 must satisfy the system (7.9) to (7.11) Moreover, if the continuous functions V, j1 and j2 verify the system (7.9) to (7.11) for all ≤ t ≤ T, then ... and the thesis holds.▀ Another related problem Now, we will consider a new non-classical initial-boundary value problem (P5) for the heat equation in the slab [0,1], which is related to the previous...

Ngày tải lên: 21/06/2014, 02:20

... variable formula, closed-form expression of the MSRL are given Finally, note that the concept of the MSRL can be used to optimize, for example, the waveform and/or the array geometry for a specific ... derive the MSRL using the lk norm for a given integer k ≥ The aim of this part is to support the endnote a, which stays that using the l1 norm computing the MSRL using the l1 norm is for the calculation ... hypothesis test and on the CRB approach The link between theses two MSRLs is also described in section “Determination of the MSRL for two sources” followed by the derivation of the MSRL closed-form...

Ngày tải lên: 21/06/2014, 03:20

... were used for a system of the generalized nonlinear Schrodinger equations, Regularized long wave RLW equations, ¨ Sine-Gordon equation, Klein-Gordon equation, Zakharov equations, Rosenau equation, ... of all the schemes are very good Hence, we propose a new conservative difference scheme for the general Rosenau-RLW equation, which simulates conservative laws 1.4 and 1.5 at the same time The outline ... continuous Assume, moreover, that there exist α > 0, for all z ∈ H, z α, and z∗ ≤ α ω z , z > Then, there exists a z∗ ∈ H such that g z∗ {ν Let Zh following νj | ν0 Theorem 2.4 There exists Un νJ ν0 νJ...

Ngày tải lên: 21/06/2014, 11:20

... + α < q + β and u0 ∈ L1 (Ω) By the so-called stability theorem with the initial data, they proved that there exists a generalized solution u(t) ∈ C([0, T ], L1 ) for 1,2 (1.2), in which u(t) satisfies ... estimates of u(t) Also the proof of the main results will be given in Section The L∞ estimates of u(t) are considered in Section The asymptotic behavior of solution for the small initial data ... loc −div((| u|m u) Then, the function u is a global weak solution of (1.1) Furthermore, it follows from Lemma 3.4 that u(t) satisfies the estimate (2.4)–(2.5) The Proof of Theorem 2.4 is now completed...

Ngày tải lên: 21/06/2014, 20:20

... K uniformly for each t ∈ R Therefore for every ε > there exists δ > such that for all X, Y ∈ K with X − Y < δ yield F b σ, X − F b σ, X

Ngày tải lên: 21/06/2014, 20:20

... theory and practice There are some results in 13–15 In this paper, we propose new trace bounds for the product of two general matrices The new trace bounds improve the recent results Then, for ... upper bounds for the trace of the product of two arbitrary real matrices We have showed that our bounds for the trace are the tightest among the parallel trace bounds in nonsymmetric case Then, we ... of Inequalities and Applications Therefore, considering the application of the trace bounds, many scholars pay much attention to estimate the trace bounds for the product of two matrices Marshall...

Ngày tải lên: 22/06/2014, 02:20

... then the conjugate A -harmonic equation becomes the form |du|p−2 du d∗ v 1.15 It is the conjugate p -harmonic equation So we can see that the conjugate p -harmonic equation and the conjugate A -harmonic ... p -harmonic type system, then we say the equation d∗ A x, a d∗ b du 1.10 is a p -harmonic type equation The following definition appears in Definition 1.3 A differential form u is a weak solution for ... Applications In this paper, we will prove the Poincar´ inequality see Theorem 2.5 and the reverse e Holder inequality for the solution to the p -harmonic type system see Theorem 3.5 Now let ¨ us see some...

Ngày tải lên: 22/06/2014, 02:20

... Dirichlet forms [6, 13] Concerning (g) we observe that in the bilinear case the Leibniz rule holds for both the arguments of the form [6, 13], but in the nonlinear case the property holds only for the ... quasi-continuous for the capacity relative to α, then (2.43) holds for q.e xo ∈ Ω We have so proved Proposition 2.6 Corollary 2.7 Let the hypothesis of Proposition 2.6 hold Then there exists a ... list now the assumptions that give the relations between the topology, the distance and the measure on X Assumption (H7 ) A distance d is defined on X, such that α(d) ≤ m in the sense of the measures...

Ngày tải lên: 22/06/2014, 22:20