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Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping

Igor Chueshov Kharkov University, Kharkov, Ukraine
Irena Lasiecka University of Virginia, Charlottesville, VA
Available Formats:
Electronic ISBN: 978-1-4704-0518-2
Product Code: MEMO/195/912.E
List Price: $80.00 MAA Member Price:$72.00
AMS Member Price: $48.00 Click above image for expanded view Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping Igor Chueshov Kharkov University, Kharkov, Ukraine Irena Lasiecka University of Virginia, Charlottesville, VA Available Formats:  Electronic ISBN: 978-1-4704-0518-2 Product Code: MEMO/195/912.E  List Price:$80.00 MAA Member Price: $72.00 AMS Member Price:$48.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 1952008; 183 pp
MSC: Primary 37; Secondary 34; 47;

The authors consider abstract nonlinear second order evolution equations with a nonlinear damping. Questions related to long time behavior, existence and structure of global attractors are studied. Particular emphasis is put on dynamics which—in addition to nonlinear dissipation— have noncompact semilinear terms and whose energy may not be necessarily decreasing. For such systems the authors first develop a general theory at the abstract level. They then apply the general theory to nonlinear wave and plate equations exhibiting the aforementioned characteristics and are able to provide new results pertaining to several open problems in the area of structure and properties of global attractors arising in this class of PDE dynamics.

• Chapters
• 1. Introduction
• 2. Abstract results on global attractors
• 3. Existence of compact global attractors for evolutions of the second order in time
• 4. Properties of global attractors for evolutions of the second order in time
• 5. Semilinear wave equation with a nonlinear dissipation
• 6. Von Karman evolutions with a nonlinear dissipation
• 7. Other models from continuum mechanics
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Volume: 1952008; 183 pp
MSC: Primary 37; Secondary 34; 47;

The authors consider abstract nonlinear second order evolution equations with a nonlinear damping. Questions related to long time behavior, existence and structure of global attractors are studied. Particular emphasis is put on dynamics which—in addition to nonlinear dissipation— have noncompact semilinear terms and whose energy may not be necessarily decreasing. For such systems the authors first develop a general theory at the abstract level. They then apply the general theory to nonlinear wave and plate equations exhibiting the aforementioned characteristics and are able to provide new results pertaining to several open problems in the area of structure and properties of global attractors arising in this class of PDE dynamics.

• Chapters
• 1. Introduction
• 2. Abstract results on global attractors
• 3. Existence of compact global attractors for evolutions of the second order in time
• 4. Properties of global attractors for evolutions of the second order in time
• 5. Semilinear wave equation with a nonlinear dissipation
• 6. Von Karman evolutions with a nonlinear dissipation
• 7. Other models from continuum mechanics
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