The Well-Posedness of the Kuramoto–Sivashinsky Equation
From MaRDI portal
Publication:3744599
DOI10.1137/0517063zbMath0606.35073OpenAlexW1964896841MaRDI QIDQ3744599
Publication date: 1986
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/0517063
stabilityexistenceuniquenessBurgers equationsviscous flowreaction-diffusionwell-posedfixed point iterationsKuramoto- Sivashinsky equationflame-propagation
Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).
Related Items (57)
Global existence for the two-dimensional Kuramoto-Sivashinsky equation with advection ⋮ Moderate deviations for stochastic Kuramoto–Sivashinsky equation ⋮ On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation ⋮ Korteweg--de Vries and Kuramoto--Sivashinsky equations in bounded domains ⋮ DISPERSIVE EFFECTS IN A MODIFIED KURAMOTO–SIVASHINSKY EQUATION ⋮ Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations ⋮ Trivial stationary solutions to the Kuramoto-Sivashinsky and certain nonlinear elliptic equations ⋮ On the Benney-Lin and Kawahara equations ⋮ On the initial-boundary value problem for a Kuramoto-Sinelshchikov type equation ⋮ Regularity criteria for the Kuramoto-Sivashinsky equation in dimensions two and three ⋮ Backward difference formulae for Kuramoto-Sivashinsky type equations ⋮ Meshless method of lines for the numerical solution of generalized Kuramoto-Sivashinsky equation ⋮ Second-order splitting combined with orthogonal cubic spline collocation method for the Kuramoto-Sivashinsky equation ⋮ Explicit estimates on the torus for the sup-norm and the crest factor of solutions of the modified Kuramoto-Sivashinky equation in one and two space dimensions ⋮ \(H^1\) solutions for a Kuramoto-Sinelshchikov-Cahn-Hilliard type equation ⋮ Investigation of the analyticity of dissipative-dispersive systems via a semigroup method ⋮ On the singular limit of a boundary delayed Kuramoto-Sivashinsky-Korteweg-de Vries equation: well-posedness and stability results ⋮ OCCURRENCE AND NON-APPEARANCE OF SHOCKS IN FRACTAL BURGERS EQUATIONS ⋮ On the dynamics of aeolian sand ripples ⋮ A study of bifurcation parameters in travelling wave solutions of a damped forced Korteweg de Vries-Kuramoto Sivashinsky type equation ⋮ Dynamical bifurcation for the Kuramoto-Sivashinsky equation ⋮ Numerical method based on the lattice Boltzmann model for the Kuramoto-Sivashinsky equation ⋮ Study of \(4^{th}\) order Kuramoto-Sivashinsky equation by septic Hermite collocation method ⋮ Convergence of a finite difference scheme for a flame/smoldering-front evolution equation and its application to wavenumber selection ⋮ ROBUST IMPLICIT DIFFERENCE APPROACH FOR THE TIME-FRACTIONAL KURAMOTO–SIVASHINSKY EQUATION WITH THE NON-SMOOTH SOLUTION ⋮ \(H^1\) solutions for a Kuramoto-Velarde type equation ⋮ Semilinear anisotropic evolution partial differential equations. ⋮ A single bounded input‐feedback control to the generalized Korteweg–de Vries–Burgers–Kuramoto–Sivashinsky equation ⋮ A non-homogeneous boundary value problem for the Kuramoto-Sivashinsky equation posed in a finite interval ⋮ Well-posedness of a two-dimensional coordinate-free model for the motion of flame fronts ⋮ High-order finite element methods for the Kuramoto-Sivashinsky equation ⋮ On a diffusion model for growth and dispersal in a population ⋮ Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations ⋮ Well-posedness and exponential stability results for a nonlinear Kuramoto-Sivashinsky equation with a boundary time-delay ⋮ Global solutions of the two-dimensional Kuramoto-Sivashinsky equation with a linearly growing mode in each direction ⋮ Existence and nonexistence of a global solution to the Kuramoto-Sivashinsky equation ⋮ Implicit-explicit multistep finite element methods for nonlinear parabolic problems ⋮ Rigorous derivation of the Kuramoto-Sivashinsky equation from a 2D weakly nonlinear Stefan problem ⋮ Some global dynamical properties of a class of pattern formation equations ⋮ Linearly implicit schemes for a class of dispersive-dissipative systems ⋮ Analyticity and Gevrey class regularity for a Kuramoto-Sivashinsky equation in space dimension two ⋮ Global well-posedness of the stochastic generalized Kuramoto-Sivashinsky equation with multiplicative noise ⋮ Quintic B-spline collocation method for numerical solution of the Kuramoto-Sivashinsky equation ⋮ Well-posedness of the classical solution for the Kuramto-Sivashinsky equation with anisotropy effects ⋮ Nonlinear adaptive boundary control of the modified generalized Korteweg-de Vries-Burgers equation ⋮ Analyticity for Kuramoto-Sivashinsky-type equations in two spatial dimensions ⋮ On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations ⋮ On the exponential stability of a nonlinear Kuramoto-Sivashinsky-Korteweg-de Vries equation with finite memory ⋮ A mesh-free numerical method for solution of the family of Kuramoto-Sivashinsky equations ⋮ Global existence and analyticity for the 2D Kuramoto-Sivashinsky equation ⋮ Well-posedness result for the Kuramoto-Velarde equation ⋮ On the solutions for a Benney-Lin type equation ⋮ Analyticity for a class of non-linear evolutionary pseudo-differential equations ⋮ Solitary wave propagation of the generalized Kuramoto-Sivashinsky equation in fragmented porous media ⋮ Well-Posedness and Asymptotics of a Coordinate-Free Model of Flame Fronts ⋮ Modelling and nonlinear boundary stabilization of the modified generalized Korteweg-de Vries-Burgers equation ⋮ Boundary linear stabilization of the modified generalized Korteweg-de Vries-Burgers equation
This page was built for publication: The Well-Posedness of the Kuramoto–Sivashinsky Equation