19052
Lecture
SoSe 13: Differentialgleichungen III - Nonlinear parabolic equations
Pavel Gurevich
Comments
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
close
- 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
Suggested reading
- 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 Class schedule
Regular appointments
Thu, 2013-04-11 10:00 - 12:00
Thu, 2013-04-18 10:00 - 12:00
Thu, 2013-04-25 10:00 - 12:00
Thu, 2013-05-02 10:00 - 12:00
Thu, 2013-05-16 10:00 - 12:00
Thu, 2013-05-23 10:00 - 12:00
Thu, 2013-05-30 10:00 - 12:00
Thu, 2013-06-06 10:00 - 12:00
Thu, 2013-06-13 10:00 - 12:00
Thu, 2013-06-20 10:00 - 12:00
Thu, 2013-06-27 10:00 - 12:00
Thu, 2013-07-04 10:00 - 12:00
Thu, 2013-07-11 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 ...
read more