Attractors of Multivalued Dynamical Processes Generated by Phase-Field Equations

DOI10.1142/S0218127403007801zbMath1063.37070OpenAlexW2029950695MaRDI QIDQ4655497

Valero, José, Melnik, Valery S., Oleksiy V. Kapustyan

Publication date: 8 March 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127403007801

zbMATH Keywords

differential inclusionsglobal attractorphase-field equationsnonautonomous multivalued dynamical system

Mathematics Subject Classification ID

Attractors (35B41) Nonlinear parabolic equations (35K55) Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators (35K85) PDEs with multivalued right-hand sides (35R70) Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30)

Related Items

On the Kneser property for some parabolic problems, Boundedness and finite-time stability for multivalued doubly-nonlinear evolution systems generated by a microwave heating problem, Weak and strong attractors for the 3D Navier-Stokes system, On the connectedness and asymptotic behaviour of solutions of reaction-diffusion systems, Robustness of nonautonomous attractors for a family of nonlocal reaction-diffusion equations without uniqueness, Weak mean random attractors for non-local random and stochastic reaction–diffusion equations, Asymptotic gain results for attractors of semilinear systems, Robustness of time-dependent attractors in \(H^1\)-norm for nonlocal problems, Attractors for nonautonomous parabolic equations without uniqueness, Global attractor and omega-limit sets structure for a phase-field model of thermal alloys, Asymptotic behaviour of nonlocal \(p\)-Laplacian reaction-diffusion problems, On L^r -regularity of global attractors generated by strong solutions of reaction-diffusion equations, Uniform trajectory attractor for non-autonomous reaction-diffusion equations with Carathéodory's nonlinearity, Optimal control and controllability of a phase field system with one control force, Asymptotic behaviour of monotone multi-valued dynamical systems, Attractors for gradient flows of nonconvex functionals and applications, Global attractor for a nonlocal \(p\)-Laplacian equation without uniqueness of solution, On global attractors of multivalued semiflows generated by the 3D Bénard system, Asymptotic behaviour of reaction-diffusion equations with non-damped impulsive effects, Autonomous and non-autonomous attractors for differential equations with delays, Global attractor for the autonomous wave equation in ℝn with continuous nonlinearity, RECENT DEVELOPMENTS IN DYNAMICAL SYSTEMS: THREE PERSPECTIVES, COMPARISON BETWEEN TRAJECTORY AND GLOBAL ATTRACTORS FOR EVOLUTION SYSTEMS WITHOUT UNIQUENESS OF SOLUTIONS, Asymptotic compactness and attractors for phase-field equations in \(\mathbb R^{3}\), Asymptotic behaviour of a phase-field model with three coupled equations without uniqueness, Analysis of a two-phase field model for the solidification of an alloy, On the Kneser property for the complex Ginzburg-Landau equation and the Lotka-Volterra system with diffusion, Pullback attractors in \(V\) for non-autonomous 2D-Navier-Stokes equations and their tempered behaviour, Global attractors of mild solutions semiflow for semilinear parabolic equation without uniqueness, Long-time behavior of a non-autonomous parabolic equation with nonlocal diffusion and sublinear terms

Cites Work

• Unnamed Item
• Solutions of evolution inclusions. I
• On solutions of evolution inclusions. II
• On the asymptotic behavior of generalized processes, with applications to nonlinear evolution equations
• On attractors of multivalued semi-flows and differential inclusions
• Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations
• Evolution equations and their trajectory attractors
• Global attractors for multivalued random semiflows generated by random differential inclusions with additive noise
• On global attractors of multivalued semiprocesses and nonautonomous evolution inclusions
• Attractors of multivalued semiflows generated by differential inclusions and their approximations
• Global attractors for multivalued random dynamical systems generated by random differential inclusions with multiplicative noise
• Attractors of parabolic equations without uniqueness