Asymptotic Stability for Diffusion with Dynamic Boundary Reaction from Ginzburg–Landau Energy

DOI10.1137/22m1469791zbMath1514.35048arXiv2201.02105MaRDI QIDQ6042077

Yuan Gao, Jean-Michel Roquejoffre

Publication date: 16 May 2023

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

Full work available at URL: https://arxiv.org/abs/2201.02105

zbMATH Keywords

metastabilityboundary stabilizationdouble well potentiallong time behavioralgebraic decay

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Long-time behavior of solutions for dynamical problems in solid mechanics (74H40)

Related Items

Uniform decay estimates for the semi-linear wave equation with locally distributed mixed-type damping via arbitrary local viscoelastic versus frictional dissipative effects

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The shape of expansion induced by a line with fast diffusion in Fisher-KPP equations
• Local and global minimizers for a variational energy involving a fractional norm
• Generation, propagation, and annihilation of metastable patterns
• Slow motion of particle systems as a limit of a reaction-diffusion equation with half-Laplacian in dimension one
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Traveling waves in a convolution model for phase transitions
• The Laplacian with Wentzell-Robin boundary conditions on spaces of continuous functions
• The Laplacian on \(C(\overline\Omega)\) with generalized Wentzell boundary conditions
• Time asymptotics of structured populations with diffusion and dynamic boundary conditions
• The influence of a line with fast diffusion on Fisher-KPP propagation
• Revisit of the Peierls-Nabarro model for edge dislocations in Hilbert space
• Long time behavior of dynamic solution to Peierls-Nabarro dislocation model
• Influence of a road on a population in an ecological niche facing climate change
• Crystal dislocations with different orientations and collisions
• Second order differential operators with Feller-Wentzell type boundary conditions
• Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting
• Relaxation times for atom dislocations in crystals
• The parabolic differential equations and the associated semigroups of transformation
• Existence and uniqueness of bounded stable solutions to the Peierls-Nabarro model for curved dislocations
• Strongly Nonlocal Dislocation Dynamics in Crystals
• The effect of a line with nonlocal diffusion on Fisher-KPP propagation
• Heat Equation with Dynamical Boundary Conditions of Reactive Type
• Long-time behavior for crystal dislocation dynamics
• The Effect on Fisher-KPP Propagation in a Cylinder with Fast Diffusion on the Boundary
• A New Method to Obtain Uniform Decay Rates for Multidimensional Wave Equations with Nonlinear Acoustic Boundary Conditions
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)
• $C_0$-semigroups generated by second order differential operators with general Wentzell boundary conditions
• Projection Method for Droplet Dynamics on Groove-Textured Surface with Merging and Splitting
• Existence and rigidity of the vectorial Peierls–Nabarro model for dislocations in high dimensions
• Layer solutions in a half‐space for boundary reactions
• Diffusion Processes in One Dimension
• Linear parabolic problems with dynamic boundary conditions in spaces of Hölder continuous functions