scholarly journals Cauchy problem for a sixth order Cahn-Hilliard type equation with inertial term

2015 ◽  
Vol 4 (3) ◽  
pp. 315-324 ◽  
Author(s):  
Aibo Liu ◽  
◽  
Changchun Liu ◽  
Keyword(s):  
Cauchy Problem ◽  
Type Equation ◽  
Sixth Order ◽  
Inertial Term

Applications of Erdélyi-Kober fractional integral for solving time-fractional Tricomi-Keldysh type equation

2020 ◽  
Vol 23 (5) ◽  
pp. 1381-1400 ◽  
Author(s):  
Kangqun Zhang
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Integral Operator ◽  
Nonlinear Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Formal Solution ◽  
Type Equation ◽  
Multiplier Theorem ◽  
Problem Of Time

Abstract In this paper we consider Cauchy problem of time-fractional Tricomi-Keldysh type equation. Based on the theory of a Erdélyi-Kober fractional integral operator, the formal solution of the inhomogeneous differential equation involving hyper-Bessel operator is presented with Mittag-Leffler function, then nonlinear equations are considered by applying Gronwall-type inequalities. At last, we establish the existence and uniqueness of L p -solution of time-fractional Tricomi-Keldysh type equation by use of Mikhlin multiplier theorem.

scholarly journals Weak Solutions for a Sixth Order Cahn-Hilliard Type Equation with Degenerate Mobility

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Aibo Liu ◽  
Changchun Liu
Keyword(s):  
Existence Result ◽  
Type Equation ◽  
Initial Boundary ◽  
Sixth Order ◽  
Surfactant Mixtures ◽  
Initial Boundary Problem ◽  
Degenerate Mobility ◽  
Oil Water ◽  
Three Space ◽  
Diffusional Mobility

We study an initial-boundary problem for a sixth order Cahn-Hilliard type equation, which arises in oil-water-surfactant mixtures. An existence result for the problem with a concentration dependent diffusional mobility in three space dimensions is presented.

On the classical solutions for a Rosenau–Korteweg-deVries–Kawahara type equation

2021 ◽  
pp. 1-23
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
Cauchy Problem ◽  
Small Amplitude ◽  
Type Equation ◽  
Discrete Systems ◽  
Finite Depth ◽  
Capillary Waves ◽  
Classical Solutions ◽  
Well Posedness ◽  
Kawahara Equation ◽  
The Cauchy Problem

The Rosenau–Korteweg-deVries–Kawahara equation describes the dynamics of dense discrete systems or small-amplitude gravity capillary waves on water of a finite depth. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem.

scholarly journals Find A General Solution Of An Equation Of The Hyperbolic Type With A Second-Order Singular Coefficient And Solve The Cauchy Problem Posed For This Equation.

2021 ◽  
Vol 25 (1) ◽  
pp. 80
Author(s):  
Karimova Shalola Musayevna ◽  
Melikuzieva Dilshoda Mukhtorjon qizi
Keyword(s):  
Cauchy Problem ◽  
General Solution ◽  
Type Equation ◽  
Second Order ◽  
Hyperbolic Type ◽  
Singular Coefficient ◽  
The Cauchy Problem

This paper presents a general solution of a hyperbolic type equation with a second-order singular coefficient and a solution to the Cauchy problem posed for this equation.

scholarly journals Cauchy problem for the complex Ginzburg-Landau type Equation with $L^{p}$-initial data

2014 ◽  
Vol 139 (2) ◽  
pp. 353-361 ◽  
Author(s):  
Daisuke Shimotsuma ◽  
Tomomi Yokota ◽  
Kentarou Yoshii
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Type Equation ◽  
Ginzburg Landau
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