On the principle of linearized stability in interpolation spaces for quasilinear evolution equations

DOI10.1007/s00605-019-01352-zzbMath1435.35051arXiv1804.10523OpenAlexW2991836912MaRDI QIDQ2297586

Christoph Walker, Bogdan-Vasile Matioc

Publication date: 20 February 2020

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.10523

zbMATH Keywords

interpolation spacesprinciple of linearized stabilityquasilinear parabolic problem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Abstract parabolic equations (35K90) Stability in context of PDEs (35B35) Quasilinear parabolic equations (35K59)

Related Items

Well-posedness of the Muskat problem in subcritical L_p-Sobolev spaces, Well-posedness and stability results for some periodic Muskat problems, A new reformulation of the Muskat problem with surface tension, Weak and classical solutions to an asymptotic model for atmospheric flows, The Muskat problem with surface tension and equal viscosities in subcritical \(L_p\)-Sobolev spaces, Boundary layer solutions to singularly perturbed quasilinear systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global solutions of abstract quasilinear parabolic equations
• Interface evolution: the Hele-Shaw and Muskat problems
• Abstract quasilinear parabolic equations
• Dynamic theory of quasilinear parabolic equations. II: Reaction-diffusion systems
• Well-posedness of the Muskat problem with \(H^2\) initial data
• On convergence of solutions to equilibria for quasilinear parabolic problems
• On quasilinear parabolic systems
• Stability, instability and center manifold theorem for fully nonlinear autonomous parabolic equations in Banach space
• Equations d'évolution abstraites non linéaires de type parabolique
• The linearization principle for the stability of solutions of quasilinear parabolic equations. I
• The Muskat problem in two dimensions: equivalence of formulations, well-posedness, and regularity results
• Critical spaces for quasilinear parabolic evolution equations and applications
• Well-posedness and stability results for a quasilinear periodic Muskat problem
• Convergence to a stationary state and stability for solutions of quasilinear parabolic equations
• Age-dependent equations with non-linear diffusion
• On normal stability for nonlinear parabolic equations
• Moving Interfaces and Quasilinear Parabolic Evolution Equations
• Nonlinear analytic semiflows
• The principle of linearized stability for quasilinear parabolic evolution equations
• Asymptotic exponential stability in quasilinear parabolic equations
• Quasilinear Evolution Equations and Parabolic Systems
• Dynamic theory of quasilinear parabolic equations—I. Abstract evolution equations
• Analyticity of the maximal solution of an abstract nonlinear parabolic equation
• Viscous displacement in porous media: the Muskat problem in 2D
• Dynamics of a free boundary problem with curvature modeling electrostatic MEMS
• Analytic semigroups and optimal regularity in parabolic problems
• Maximal regularity in continuous interpolation spaces and quasilinear parabolic equations