[PDF] Top 20 The entropy weak solution to a generalized Degasperis Procesi equation

... all weak traveling wave ...the Degasperis-Procesi equation and other shallow water equations, the reader is referred to [–] and the references ... See full document

... KdV equation from different ...(CH) equation and the weakly dissipative DP equation were studied in [–] and [–], ...b-family equation. Recently, some results for a weakly dissipative ... See full document

... are weak solutions in the distributional sense and shown to be stable in [17, ...a solution that remains bounded while its slope becomes unbounded in finite time) [11–14, 25, 29, ... See full document

... In this section we recall some elementary results which we want to use in this paper. We list them and skip their proofs for conciseness. Local well-posedness for equation (.) can be obtained by Kato’s theory ... See full document

... global weak solutions and blow-up structures for ...a generalized periodic Degasperis-Procesi equation was obtained in ...the Degasperis-Procesi () and other shallow ... See full document

... and Degasperis-Procesi equations (see ...Novikov equation with a peak ...Novikov equation associated with the initial value is locally well-posed in Sobolev space H s with s >   by using ... See full document

... uniqueness of analytic solutions for Eq. () are obtained in []. It is worthy to mention that if the Sobolev index s ≥  and sign conditions hold, the orbit invariants are applied to show the existence of periodic ... See full document

... the generalized shallow water equa- tion with a viscous term, which includes the viscous Camassa–Holm equation and vis- cous Degasperis–Procesi equation as special ...optimal ... See full document

... In the following, we will give the conservation law in some case for Eq. () in Section . The proof of existence for the local strong solution and its stability to Eq. () are given in Section  and Section , ... See full document

... (dCH) equation for which 𝛾 = 2 and the Degasperis–Procesi (DP) equation for which 𝛾 = ...respectively. Weak travelling-wave solutions of the CH and DP equations, including exotic ... See full document

... a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless ... See full document

... integrable equation with peakon ...integrable equation with ...Global weak solutions to a new periodic integrable equation with peakon ... See full document

... the generalized Degasperis-Procesi equation possesses the peaked solitary wave which is the weak solution to the generalized Degasperis-Procesi ...the ... See full document

... changes along with the choice of the general characteristic function. The simplest one is the distance function from the boundary d(x) = dist(x, ∂Ω ), in this case, ∇d = n is the inner normal vector of Ω. The novelty of ... See full document

... The weak derivative bears many properties the normal derivative has such as linearity (with respect to addition and constant multiplication); u ∈ W k,p ⇒ D α u ∈ W k−|α|,p for |α| ≤ k; product rule and chain ... See full document

... (weak) solution. Then the generalized solution u ∈ G R × [0, ∞) is associated with ...continuous solution on the initial ...distributional solution, in general. Yet the ... See full document

... vibration equation for vis- coelastic damped structures with a springpot ...[35] generalized the standard linear solid (Zener model) with Caputo fractional derivative, which was different from previously ... See full document

... Equation (1.6) is always degenerate on the boundary. This is the most characteristic feature of equation (1.6) different from equation (1.3). Let us give a further explanation. For two weak ... See full document

... It is known that the KS equation has travelling wave solution in terms of hyperbolic tangent function, whereas the KdVB equation has travelling wave solution invo[r] ... See full document

... for generalized Burger’s-Fisher ...the generalized Burger’s-Fisher ...the solution of the generalized Burger’s-Fisher ...for generalized Burger’s-Huxley and Burger’s-Fisher ... See full document