Nonuniqueness and Uniqueness in the Initial-Value Problem for Burgers’ Equation

DOI10.1137/0527038zbMath0852.35123OpenAlexW2167352438MaRDI QIDQ4880242

Daniel B. Dix

Publication date: 4 June 1996

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/5623543ce6f18dfaa10ef1b3a000732c97bcfa69

zbMATH Keywords

Sobolev spacesuniquenessBurgers' equationinitial-value problemnonuniqueness

Mathematics Subject Classification ID

Related Items (46)

Numerical efficiency of some exponential methods for an advection–diffusion equation ⋮ Well-posedness and regularity of the generalized Burgers equation in periodic Gevrey spaces ⋮ A construction of two different solutions to an elliptic system ⋮ Nonhomogeneous boundary value problems for the complex Ginzburg–Landau equation posed on a finite interval ⋮ The IVP for a nonlocal perturbation of the Benjamin-Ono equation in classical and weighted Sobolev spaces ⋮ Sharp well-posedness for the Chen-Lee equation ⋮ Asymptotic stability of traveling wave solutions for nonlocal viscous conservation laws with explicit decay rates ⋮ \(L_p\)-regularity theory for semilinear stochastic partial differential equations with multiplicative white noise ⋮ Local and global well-posedness for the 2D Zakharov-Kuznetsov-Burgers equation in low regularity Sobolev space ⋮ A regularity theory for stochastic generalized Burgers' equation driven by a multiplicative space-time white noise ⋮ Well-posedness results and dissipative limit of high dimensional KdV-type equations ⋮ Global existence and finite-time blow-up for a nonlinear nonlocal evolution equation ⋮ On nonlinear conservation laws with a nonlocal diffusion term ⋮ The IVP for a periodic generalized ZK equation ⋮ Fractional derivative estimates in Gevrey spaces, global regularity and decay for solutions to semilinear equations in \(\mathbb R^n\) ⋮ Well-posedness of the stochastic KdV-Burgers equation ⋮ Self-similar solutions to nonlinear Dirac equations and an application to nonuniqueness ⋮ Well-posedness of the generalized Benjamin-Ono-Burgers equations in Sobolev spaces of negative order ⋮ The ADMB-KdV equation in a time-weighted space ⋮ Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations ⋮ Quadratic forms for the 1-D semilinear Schrödinger equation ⋮ On the well-posedness of higher order viscous Burgers' equations ⋮ Sharp local well-posedness of KdV type equations with dissipative perturbations ⋮ On the low regularity of the Benney-Lin equation ⋮ Parabolic equations with conservative nonlinear term and singular initial data ⋮ Well-posedness result for the Ostrovsky, Stepanyams and Tsimring equation at the critical regularity ⋮ An explicit solution of Burgers equation with stationary point source ⋮ Non-homogeneous boundary value problems for the Korteweg-de Vries and the Korteweg-de Vries-Burgers equations in a quarter plane ⋮ Sharp ill-posedness and well-posedness results for the KdV-Burgers equation: The periodic case ⋮ The IVP for the evolution equation of wave fronts in chemical reactions in low-regularity Sobolev spaces ⋮ On the sharp local well-posedness for the modified Ostrovsky, Stepanyams and Tsimring equation ⋮ Well-posedness for a perturbation of the KdV equation ⋮ Well-posedness of the fractional Ginzburg–Landau equation ⋮ On the low regularity of the modified Korteweg-de Vries equation with a dissipative term ⋮ On the generalized Burgers-Huxley equation: existence, uniqueness, regularity, global attractors and numerical studies ⋮ A priori bounds for KdV equation below \(H^{- \frac{3}{4}}\) ⋮ Well-posedness of the ADMB-KdV equation in Sobolev spaces of negative indices ⋮ Singular asymptotic expansions and delta waves for Burgers' equation ⋮ Fractal Burgers equations ⋮ Asymptotic behavior for the viscous Burgers equation with a stationary source ⋮ Well-posedness of a semilinear heat equation with weak initial data ⋮ Well-posedness of the generalized Burgers equation on a finite interval ⋮ A non-homogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain. II. ⋮ The Colombeau generalized nonlinear analysis and the Schwartz linear distribution theory ⋮ Ill-posedness for the nonlinear Schrödinger equation with quadratic non-linearity in low dimensions ⋮ Scaling in nonlinear parabolic equations

This page was built for publication: Nonuniqueness and Uniqueness in the Initial-Value Problem for Burgers’ Equation