Global Attractor for Sectorial Evolutionary Equation
Copyright policy )Global Attractor for Sectorial Evolutionary Equation
Let \(A\) be a sectorial operator with compact resolvent in an appropriate Banach space and consider the evolution equation \(\dot u + Au = F(u)\), \(t > 0\), \(u(0) = u_0\). The authors show that this problem generates a dissipative semigroup whenever an appropriate introductory estimate for solutions is known. Such an estimate is then shown to be sufficient for existence of a global attractor. Examples illustrate the authors ideas.
- Silesian University in Opava Czech Republic
- Institute of Mathematics Poland
- Medical University of Silesia Poland
- Polish Academy of Sciences Poland
evolution equation, sectorial operator, Initial value problems for linear higher-order PDEs, dissipative semigroup, global attractor, Nonlinear differential equations in abstract spaces, Attractors of solutions to ordinary differential equations, Analysis, Higher-order parabolic equations
evolution equation, sectorial operator, Initial value problems for linear higher-order PDEs, dissipative semigroup, global attractor, Nonlinear differential equations in abstract spaces, Attractors of solutions to ordinary differential equations, Analysis, Higher-order parabolic equations
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