19052
Vorlesung
SoSe 13: Differentialgleichungen III - Nonlinear parabolic equations
Pavel Gurevich
Kommentar
Topics:
- 1. Sectorial operators. Analytic semigroups
- 2. Fractional powers of sectorial operators
- 3. Invariant subspaces and exponential bounds
- 4. Cauchy problem for linear parabolic equations
- 5. Cauchy problem for semilinear parabolic equations. Local existence
and uniqueness
- 6. Continuous and differentiable dependence of solutions
- 7. Lyapunov function
- 8. Stability and instability by linear approximation
- 9. Saddle-point property (stable/unstable manifold)
- 10. Equilibria of the Chafee-Infante problem
Schließen
- 1. Sectorial operators. Analytic semigroups
- 2. Fractional powers of sectorial operators
- 3. Invariant subspaces and exponential bounds
- 4. Cauchy problem for linear parabolic equations
- 5. Cauchy problem for semilinear parabolic equations. Local existence and uniqueness
- 6. Continuous and differentiable dependence of solutions
- 7. Lyapunov function
- 8. Stability and instability by linear approximation
- 9. Saddle-point property (stable/unstable manifold)
- 10. Equilibria of the Chafee-Infante problem
Literaturhinweise
- 1. D. Henry. Geometric theory of semilinear parabolic equations}, Lecture Notes in Mathematics. Vol 840. Berlin-New York, Springer. 1981.
- 2. A. Pazy. Semigroups of linear operators and applications to partial differential equations. Appl. Math. Sci., Vol. 44. Springer, New York, 1983.
- 3. K. Yosida. Functional Analysis. Berlin-Heidelbert-New York, Springer. 1980.
13 Termine
Regelmäßige Termine der Lehrveranstaltung
Do, 11.04.2013 10:00 - 12:00
Do, 18.04.2013 10:00 - 12:00
Do, 25.04.2013 10:00 - 12:00
Do, 02.05.2013 10:00 - 12:00
Do, 16.05.2013 10:00 - 12:00
Do, 23.05.2013 10:00 - 12:00
Do, 30.05.2013 10:00 - 12:00
Do, 06.06.2013 10:00 - 12:00
Do, 13.06.2013 10:00 - 12:00
Do, 20.06.2013 10:00 - 12:00
Do, 27.06.2013 10:00 - 12:00
Do, 04.07.2013 10:00 - 12:00
Do, 11.07.2013 10:00 - 12:00
Topics:
1. Sectorial operators. Analytic semigroups 2. Fractional powers of sectorial operators 3. Invariant subspaces and exponential bounds 4. Cauchy problem for linear parabolic ...
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