On the Cauchy problem for a Sobolev-type equation with quadratic non-linearity

2011 ◽  
Vol 75 (5) ◽  
pp. 871-887
Author(s):  
Anatoly I Aristov
Keyword(s):  
Cauchy Problem ◽  
Type Equation ◽  
Sobolev Type ◽  
The Cauchy Problem ◽  
Sobolev Type Equation

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.

On a nonlinear Sobolev type equation

2005 ◽  
Vol 41 (1) ◽  
pp. 146-149 ◽  
Author(s):  
I. A. Shishmarev
Keyword(s):  
Type Equation ◽  
Sobolev Type ◽  
Sobolev Type Equation

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.

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