PHD Course on
Qualitative Properties of Solutions to
Nonlinear Parabolic Boundary Value Problems

 Dr. Monica Marras
University of Cagliari
Department of Mathematics and Computer Science

Plan of the course

19 October 2016, 14:00-15:00, room 478

DECAY IN TIME AND CONTINUOUS DEPENDENCE OF SOLUTIONS TO NONLINEAR PARABOLIC BOUNDARY VALUE PROBLEMS

ABSTRACT: For a class of nonlinear parabolic problems we introduce conditions on the geometry of the spatial domain and on data to insure that the solution and its gradient decay exponentially in time. We also show continuous dependence on initial data for solutions of such problems, when Robin conditions are prescribed on the boundary.

20 October 2016, 14:00-15:00, room 478

GLOBAL EXISTENCE OF SOLUTIONS TO NONLINEAR PARABOLIC BOUNDARY VALUE PROBLEMS

ABSTRACT: For some classes of nonlinear parabolic problems under different boundary conditions and time dependent coefficients, we investigate the influence of the data on the behavior of the solution in order to obtain global existence.

21 October 2016, 14:00-15:00, room 478

BLOW-UP IN INFINITE TIME OF SOLUTIONS TO NONLINEAR PARABOLIC BOUNDARY VALUE PROBLEMS

ABSTRACT: We present a method, based on a suitable energy function,that allows us to study the blow-up phenomena for the solutions to some nonlinear parabolic problems. Conditions on data are introduced, sufficient to obtain explicit upper and lower bounds for the blow-up time. Extensions on systems are presented.