The Homogeneous Flow

2018 ◽  
Author(s):  
Ercüment H. Ortaçgil
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Second Order ◽  
Initial Condition ◽  
Homogeneous Flow ◽  
Short Time

In this chapter, a second-order nonlinear evolution equation is constructed that starts with any parallelism as initial condition and flows in the direction of a parallelism with vanishing curvature. The existence of unique short-time solutions is proved.

scholarly journals Damped second order flow applied to image denoising

2019 ◽  
Vol 84 (6) ◽  
pp. 1082-1111 ◽  
Author(s):  
G Baravdish ◽  
O Svensson ◽  
M Gulliksson ◽  
Y Zhang
Keyword(s):  
Evolution Equation ◽  
Image Denoising ◽  
Nonlinear Evolution Equation ◽  
Numerical Experiments ◽  
Nonlinear Evolution ◽  
Second Order ◽  
Order Flow ◽  
Numerical Implementation ◽  
Energy Functionals

Abstract In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of an image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementation, based on the Störmer–Verlet method, a discrete DF, SV-DDF, is developed. The convergence of SV-DDF is studied as well. Several numerical experiments, as well as a comparison with other methods, are provided to demonstrate the efficiency of SV-DDF.

scholarly journals On nonlinear evolution equation of second order in Banach spaces

2018 ◽  
Vol 16 (1) ◽  
pp. 268-275
Author(s):  
Kamal N. Soltanov
Keyword(s):  
Differential Equation ◽  
Evolution Equation ◽  
Banach Spaces ◽  
Traffic Flow ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Second Order ◽  
Nonlinear Hyperbolic Equation ◽  
Existence Of A Solution ◽  
Special Case

AbstractHere we study the existence of a solution and also the behavior of the existing solution of the abstract nonlinear differential equation of second order that, in particular, is the nonlinear hyperbolic equation with nonlinear main parts, and in the special case, is the equation of the type of equation of traffic flow.

scholarly journals Lump Solutions, Multi Lump Solutions and More Soliton Solutions of a Novel (2+1)-dimensional Nonlinear Evolution Equation

2021 ◽  
Author(s):  
Hongcai Ma ◽  
Shupan Yue ◽  
Yidan Gao ◽  
Aiping Deng
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Bilinear Method ◽  
Test Function ◽  
Lump Solutions ◽  
Hirota Bilinear ◽  
Test Function Method

Abstract Exact solutions of a new (2+1)-dimensional nonlinear evolution equation are studied. Through the Hirota bilinear method, the test function method and the improved tanh-coth and tah-cot method, with the assisstance of symbolic operations, one can obtain the lump solutions, multi lump solutions and more soliton solutions. Finally, by determining different parameters, we draw the three-dimensional plots and density plots at different times.

A NONLINEAR EVOLUTION EQUATION IN AN ORDERED SPACE, ARISING FROM KINETIC THEORY

2007 ◽  
Vol 09 (02) ◽  
pp. 217-251
Author(s):  
CECIL P. GRÜNFELD
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Sufficient Conditions ◽  
Existence Theory ◽  
The Cauchy Problem ◽  
Ordered Space ◽  
Coagulation Equation ◽  
Boltzmann Model ◽  
Classical Boltzmann Equation

We investigate the Cauchy problem for a nonlinear evolution equation, formulated in an abstract Lebesgue space, as a generalization of various Boltzmann kinetic models. Our main result provides sufficient conditions for the existence, uniqueness, and positivity of global in time solutions. The analysis extends nontrivially monotonicity methods, originally developed in the context of the existence theory for the classical Boltzmann equation in L1. Our application examples are Smoluchowski's coagulation equation, a Povzner-like equation with dissipative collisions, and a Boltzmann model with chemical reactions, for which we obtain a unitary existence theory, with improved results, compared to the literature.

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