Results 41 to 50 of about 1,195 (85)

A LIPSCHITZ METRIC FOR THE CAMASSA–HOLM EQUATION

Forum of Mathematics, Sigma, 2020
We analyze stability of conservative solutions of the Cauchy problem on the line for the Camassa–Holm (CH) equation. Generically, the solutions of the CH equation develop singularities with steep gradients while preserving continuity of the solution ...
JOSÉ A. CARRILLO, KATRIN GRUNERT, HELGE HOLDEN   +2 more
doaj   +1 more source

NUMERICAL APPROXIMATION OF SPECTRUM FOR VARIABLE COEFFICIENTS EULER-BERNOULLI BEAMS UNDER A FORCE CONTROL IN POSITION AND VELOCITY

, 2017
In this paper, we use asymptotic techniques and the finite differences method to study the spectrum of differential operator arising in exponential stabilization of Euler-Bernoulli beam with nonuniform thickness or density that is clamped at one end and ...
K.A.A. Hermith, C. Adama, T. K. Augustin
semanticscholar   +1 more source

Sharp Liouville Theorems

Advanced Nonlinear Studies, 2021
Consider the equation div⁡(φ2⁢∇⁡σ)=0{\operatorname{div}(\varphi^{2}\nabla\sigma)=0} in ℝN{\mathbb{R}^{N}}, where φ>0{\varphi>0}. Berestycki, Caffarelli and Nirenberg proved in [H. Berestycki, L. Caffarelli and L. Nirenberg, Further qualitative properties
Villegas Salvador
doaj   +1 more source

A variety of soliton solutions for the fractional Wazwaz-Benjamin-Bona-Mahony equations

Results in Physics, 2019
In the present paper, the new three-dimensional modified Benjamin-Bona-Mahony equations recently introduced are analyzed with the introduction of the spatial and temporal fractional order derivatives using conformable fractional derivative.
Aly R. Seadawy, Khalid K. Ali, R.I. Nuruddeen   +2 more
doaj   +1 more source

GLOBAL NEARLY-PLANE-SYMMETRIC SOLUTIONS TO THE MEMBRANE EQUATION

Forum of Mathematics, Pi, 2020
We prove that any simple planar travelling wave solution to the membrane equation in spatial dimension $d\geqslant 3$ with bounded spatial extent is globally nonlinearly stable under sufficiently small compactly supported perturbations, where the ...
LEONARDO ABBRESCIA, WILLIE WAI YEUNG WONG   +1 more
doaj   +1 more source

STABILITY ANALYSIS OF PARTIAL DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENTS

, 2018
In this paper, the analytical stability of a partial differential equation with piecewise constant arguments is considered. By using the theory of separation of variables in matrix form and the Fourier method, the sufficient conditions under which the ...
Qi Wang
semanticscholar   +1 more source

Critical Exponents of Semilinear Equations via the Feynman-Kac Formula [PDF]

, 2007
2000 Mathematics Subject Classification: 60H30, 35K55, 35K57 ...
Alfredo Lopez-Mimbela, Jose, T. Kolkovska, Ekaterina   +1 more
core  

Stability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-Bona-Mahony Type [PDF]

, 2003
2000 Mathematics Subject Classification: 35B35, 35B40, 35Q35, 76B25, 76E30.This paper concerns the orbital stability and instability of solitary waves of the system of coupling equations of Benjamin-Bona-Mahony type.
Hakkaev, Sevdzhan
core  

An incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equations

, 2014
We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to
Chae, Dongho, Constantin, Peter, Wu, Jiahong   +2 more
core   +1 more source

Existence and nonexistence of solutions for the generalized Camassa-Holm equation

Advances in Differential Equations, 2014
In this paper, we study the Cauchy problem of a generalized Camassa-Holm equation. It is shown that the equation is locally well posed when the initial data are sufficiently smooth.
Xiujuan Pan, S. Kang, Young Chel Kwun
semanticscholar   +1 more source