Periodic stochastic high-order Degasperis–Procesi equation with cylindrical fBm

2019 ◽  
Vol 19 (06) ◽  
pp. 1950043 ◽  
Author(s):  
Yong Chen ◽  
Hongjun Gao ◽  
Jianhua Huang
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Time Variable ◽  
High Order ◽  
Hurst Parameter ◽  
Local Existence And Uniqueness ◽  
Uniqueness Of The Solution ◽  
Stochastic Term ◽  
Bourgain Space

This paper studies the periodic stochastic high-order Degasperis–Procesi (DP) equation driven by a cylindrical fractional Brownian motion (fBm) which is white in space. And it has the covariance with Hurst parameter [Formula: see text] in the time variable. The local existence and uniqueness of the solution [Formula: see text] in [Formula: see text] with [Formula: see text] are proved by fixed point theorem combined with the stochastic term estimations in the Besov-type Bourgain space [Formula: see text] and the second iteration of non-linear term.

scholarly journals Exponential decay of solutions with \(L^{p}\)-norm for a class to semilinear wave equation with damping and source terms

2020 ◽  
Vol 4 (2) ◽  
pp. 123-131
Author(s):  
Amar Ouaoua ◽  
◽  
Messaoud Maouni ◽  
Aya Khaldi ◽  
◽  
...  
Keyword(s):  
Wave Equation ◽  
Lyapunov Function ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Local Solution ◽  
Initial Value ◽  
Local Existence And Uniqueness ◽  
Decay Of Solutions ◽  
Uniqueness Of The Solution ◽  
Damping And Source Terms

In this paper, we consider an initial value problem related to a class of hyperbolic equation in a bounded domain is studied. We prove local existence and uniqueness of the solution by using the Faedo-Galerkin method and that the local solution is global in time. We also prove that the solutions with some conditions exponentially decay. The key tool in the proof is an idea of Haraux and Zuazua with is based on the construction of a suitable Lyapunov function.

scholarly journals Positive global solutions for a general model of size-dependent population dynamics

2000 ◽  
Vol 5 (3) ◽  
pp. 191-206 ◽  
Author(s):  
Nobuyuki Kato
Keyword(s):  
Growth Rate ◽  
Existence And Uniqueness ◽  
General Type ◽  
Local Existence ◽  
Global Solutions ◽  
Structured Population Models ◽  
Size Dependent ◽  
Structured Population ◽  
Local Existence And Uniqueness ◽  
Uniqueness Of The Solution

We study size-structured population models of general type which have the growth rate depending on the size and time. The local existence and uniqueness of the solution have been shown by Kato and Torikata (1997). Here, we discuss the positivity of the solution and global existence as well asL ∞solutions.

Local wellposedness in Sobolev space for the inhomogeneous non-resistive MHD equations on general domain

2017 ◽  
Vol 19 (06) ◽  
pp. 1650055
Author(s):  
Weiren Zhao
Keyword(s):  
Sobolev Space ◽  
Initial Data ◽  
Bounded Domain ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Mhd Equations ◽  
General Domain ◽  
Local Existence And Uniqueness ◽  
Uniqueness Of The Solution ◽  
Local Wellposedness

In this paper, we prove the local existence and uniqueness of the solution with discontinuous density for the inhomogeneous non-resistive magnetohydrodynamics (MHD) equations on a [Formula: see text] bounded domain [Formula: see text] or [Formula: see text], if the initial data [Formula: see text] with [Formula: see text] satisfies [Formula: see text].

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

scholarly journals Local and Global Existence of Solution for Love Type Waves with Past History

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1998
Author(s):  
Mohamed Biomy ◽  
Khaled Zennir ◽  
Ahmed Himadan
Keyword(s):  
Existence And Uniqueness ◽  
Past History ◽  
Local Existence ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Linearization Method ◽  
Weak Compactness ◽  
Existence Of Solution ◽  
Local Existence And Uniqueness ◽  
Initial Boundary Value

In this paper, we consider an initial boundary value problem for nonlinear Love equation with infinite memory. By combining the linearization method, the Faedo–Galerkin method, and the weak compactness method, the local existence and uniqueness of weak solution is proved. Using the potential well method, it is shown that the solution for a class of Love-equation exists globally under some conditions on the initial datum and kernel function.

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