We analyze the long-time asymptotics for the Degasperis- Procesi equation on the half-line. By applying nonlinear steepest descent techniques to an associated 3 x 3-matrix valued Riemann-Hilbert ...problem, we find an explicit formula for the leading order asymptotics of the solution in the similarity region in terms of the initial and boundary values.
In this paper, the Degasperis–Procesi (DP) equation which contains nonlinear high order derivatives and discontinuous solutions is recast to its equivalent form: u−P. Based on the equivalent ...formulation of DP equation, a new numerical method is presented. The multi-quadric (MQ) quasi-interpolation method coupled with finite difference method is applied to approximate the spatial derivatives and the third order TVD method is used to approximate the time derivative. Several examples are presented to demonstrate the effectiveness of the proposed method.
We analyze a class of initial-boundary value problems for the Degasperis–Procesi equation on the half-line. Assuming that the solution u(x,t) exists, we show that it can be recovered from its initial ...and boundary values via the solution of a Riemann–Hilbert problem formulated in the plane of the complex spectral parameter k.
In this paper we study several qualitative properties of the Degasperis–Procesi equation. We first established the precise blow-up rate and then determine the blow-up set of blow-up strong solutions ...to this equation for a large class of initial data. We finally prove the existence and uniqueness of global weak solutions to the equation provided the initial data satisfies appropriate conditions.
Boris Krajnc je bil prvi habilitirani učitelj ljubljanske univerze za področje biokemije – imenovanje v naziv docenta je datirano s 7. januarjem 1946. Vendar se je Krajnčeva življenjska pot zelo ...hitro končala, saj so ga 27. oktobra 1947 aretirali in 26. aprila 1948 na montiranem dachauskem procesu obsodili na smrt. Ustrelili naj bi ga 12. maja 1948, starega 34 let. Krajnčeva življenjska zgodba je tesno povezana z delom več slovenskih kemikov, ki so bili kot zaporniki v koncentracijskem taborišču Dachau izbrani za tehnično pomoč pri izvedbah poskusov na ljudeh ali pri delu v kliničnem laboratoriju. Na povojnih dachauskih procesih v Ljubljani je bilo skupaj obsojenih 8 kemikov, od teh jih je bilo 5 obsojenih na smrt in ustreljenih. V kasnejših presojah dachauskih procesov se je izkazalo, da so bile obtožnice skonstruirane, priznanja pa pridobljena s krutimi zasliševalskimi metodami, zato so bile vse sodbe razveljavljene. Po emigraciji encimatika Richarda Klemna ter pregonu Maksa Samca in Marte Blinc z univerze je bil Boris Krajnc tisti, ki naj bi skrbel za biokemijo na Tehniški fakulteti. Po njegovi smrti je nekaj let biokemijo predaval Krajnčev mlajši kolega Dušan Stucin z Medicinske fakultete, potem pa biokemije več let ni bilo v kemijskem kurikulumu.
Considered herein are the generalized Camassa–Holm and Degasperis–Procesi equations in the spatially periodic setting. The precise blow-up scenarios of strong solutions are derived for both of ...equations. Several conditions on the initial data guaranteeing the development of singularities in finite time for strong solutions of these two equations are established. The exact blow-up rates are also determined. Finally, geometric descriptions of these two integrable equations from non-stretching invariant curve flows in centro-equiaffine geometries, pseudo-spherical surfaces and affine surfaces are given.
We improve the decay argument by Bona and Li (1997) 5 for solitary waves of general dispersive equations and illustrate it in the proof for the exponential decay of solitary waves to steady ...Degasperis-Procesi equation in the nonlocal formulation. In addition, we give a method which confirms the symmetry of solitary waves, including those of the maximum height. Finally, we discover how the symmetric structure is connected to the steady structure of solutions to the Degasperis-Procesi equation, and give a more intuitive proof for symmetric solutions to be traveling waves. The improved argument and new method above can be used for the decay rate of solitary waves to many other dispersive equations and will give new perspectives on symmetric solutions for general evolution equations.
In this work we present new results on the convergence of diagonal sequences of certain mixed type Hermite-Padé approximants of a Nikishin system. The study is motivated by a mixed Hermite-Padé ...approximation scheme used in the construction of solutions of a Degasperis-Procesi peakon problem and germane to the analysis of the inverse spectral problem for the discrete cubic string.
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