2024 Fornberg-whitham

Fornberg-whitham

Author: hmxr

August undefined, 2024

WebJun 15, 2016 · In this paper, we show that the Fornberg–Whitham equation is Well-posed in Sobolev spaces H s, for s > 3 / 2, and in the periodic case.We then show that the Well-posedness is sharp in the sense that the continuity of the data-to-solution map is not better than continuous by using the method of approximate solutions. WebSep 24, 2024 · We know that the dynamic properties of the Fornberg–Whitham equation are related to those of the Camassa–Holm (CH) , Degasperis–Procesi (DP) , and Novikov …

The well-posedness, blow-up, and traveling waves for a two …

WebDec 15, 2024 · Classical Solutions of the Fornberg-Whitham Equation Georgia Burkhalter, Ryan C. Thompson, Madison Waldrep In this paper, we prove well-posedness in (a.k.a. classical solutions) of the Fornberg-Whitham equation. To achieve this objective, we study its weak formulation under a Lagrangian framework. WebMay 31, 2024 · In this paper, the two-component Fornberg-Whitham system is studied. We firstly investigate the well-posedness in classical Sobolev Space and show a blow-up scenario by local-in-time a priori estimates, then we present some sufficient conditions on the initial data to lead to wave breaking. Furthermore, we establish analytically the … h1b-cap

[2107.01357] Continuity properties of the data-to-solution map …

WebJan 20, 2024 · In this paper, an analytical technique is proposed to determine the exact solution of fractional order modified Fornberg–Whitham equation. Since exact solution of fractional Fornberg–Whitham equation is unknown, first integral method has been applied to determine exact solutions. The solitary wave solution of fractional modified … WebDec 1, 2024 · Abstract This paper is devoted to studying wave breaking phenomena for the Fornberg–Whitham equation. Making use of the structure and the conservation quantity … brack collier jmu

[2107.10442] The well-posedness, ill-posedness and non-uniform ...

Whitham equation - HandWiki

WebIn this paper, we investigate the wave breaking for the Fornberg-Whitham (FW) equation. Based on blow-up analysis of a Riccati-type inequality with a t-dependent function, which … WebIn the 1960s and 1970s, to describe the evolution of water waves, Whitham and Fornberg proposed the so-called Whitham-Fornberg (FW) equation [22], [7] (1) ⁎ as a shallow … h1b by employerWebJul 3, 2024 · Abstract: This work studies a two-component Fornberg-Whitham (FW) system, which can be considered as a model for the propagation of shallow water waves. It's known that its solutions depend continuously on their initial data from the local well-posedness result. In this paper, we further show that such dependence is not uniformly … brack chocolate

"WebFeb 20, 2024 · In this paper, we present a new method to prove that the data-to-solution map for the two-component Fornberg–Whitham is not uniformly continuous from any bounded subset in \(H^s(\mathbb {R})\times H^{s-1}(\mathbb {R})\) with \(s>3/2\) and further to show that this data-to-solution map is nowhere-uniform continuity in the same space. " - Fornberg-whitham

Fornberg-whitham

WebApr 15, 2024 · In this paper, we investigate the wave breaking for the Fornberg-Whitham (FW) equation. Based on blow-up analysis of a Riccati-type inequality with a t … WebSep 24, 2024 · We know that the dynamic properties of the Fornberg–Whitham equation are related to those of the Camassa–Holm (CH) [ 9 ], Degasperis–Procesi (DP) [ 10 ], and Novikov equations [ 11 ]. The four types of equations possess the peakon solutions. Here, we recall several works on the study of the CH, DP, and Novikov equations.

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WebJun 16, 2024 · Abstract. This article is dealing with the analytical solution of Fornberg–Whitham equations in fractional view of Caputo operator. The effective method … WebApr 1, 2024 · In this paper, the two-component Fornberg–Whitham system is studied. We first investigate the local well-posedness in classical Sobolev space and establish a blow-up criterion by a local-in-time priori estimate, and then, we give some sufficient conditions on the initial data to lead to wave breaking.

WebDec 1, 2009 · An analytical algorithm for nonlinear fractional Fornberg–Whitham equation arising in wave breaking based on a new iterative method Article Full-text available Nov 2013 Dr. Sunil Kumar View Show... WebJul 6, 2024 · Abstract. This paper is devoted to studying wave breaking phenomena for the Fornberg–Whitham equation. Making use of the structure and the conservation quantity …

WebFor a certain choice of the kernel K(x − ξ) it becomes the Fornberg–Whitham equation. Contents. 1 Water waves; 2 Notes and references. 2.1 Notes; 2.2 References; Water waves. Using the Fourier transform (and its inverse), with respect to the space coordinate x and in terms of the wavenumber k: WebJun 18, 2015 · On the analytical solution of Fornberg–Whitham equation with the new fractional derivative O. Iyiola, Gbenga O. Ojo Published 18 June 2015 Mathematics Pramana Motivated by the simplicity, natural and efficient nature of the new fractional derivative introduced by R Khalil et al in J. Comput. Appl.

WebMay 24, 2024 · Recently, Holmes and Thompson [] proved the well-posedness of Eq. () in the Besov space in the periodic and nonperiodic cases and established a Cauchy–Kowalevski-type theorem for Eq. () to show the existence and uniqueness of analytic solutions.The blow-up criterion for the solutions is given in [].Using several …

WebJan 25, 2024 · Introduction. The following Fornberg-Whitham (FW) model W t − W t x x − W x + 3 2 W W x = 9 2 W x W x x + 3 2 W W x x x, (t, x) ∈ R + × R is an equation to sketch the dynamics of shallow water waves in Fornberg and Whitham [5]. Eq. (1) has the peakon solution W (t, x) = 8 9 e − 1 2 x − 4 3 t .Holmes and Thompson [13] investigate local … h1b cap applicationWebJun 18, 2015 · Math. 264, 65 (2014), analytical solution of space-time fractional Fornberg–Whitham equation is obtained in series form using the relatively new method called q-homotopy analysis method (q-HAM).... h1b by countryWebJul 22, 2024 · Title: The well-posedness, ill-posedness and non-uniform dependence on initial data for the Fornberg-Whitham equation in Besov spaces. Authors: Yingying Guo. Download PDF brack.ch/plusWebApr 1, 2011 · In this paper, He’s variational iteration method (VIM) is applied to solve the Fornberg–Whitham type equations. The VIM provides fast converged approximate solutions to nonlinear equations... brack collierWebOct 1, 2024 · We investigate multiwave, homoclinic breather, M-shaped, Kink cross-rational, periodic cross kink solutions for the nonlinear generalized Fornberg–Whitham (gFW)-equation by using appropriate polynomial function schemes.We also obtain some interactions for governing model including; interaction of M-shaped soliton with single e x … h1b cap 2024 resultsWebMay 24, 2024 · Fornberg, G., Whitham, G.B.: A numerical and theoretical study of certain nonlinear wave phenomena. Philos. Trans. R. Soc. Lond. Ser. A 289, 373–404 (1978) … h1b by stateWebthe Fornberg-Whitham equation to the two-component system. Unlike the CH system (equa- tion) or DP system (equation), they possess inﬁnitely many conserved … brack cloppenburg