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| Jorge Salazar (CMAF Lisboa, Univ. de Evora) | WPI seminar room | Thu, 14. Oct 04, 15:00 |
| Viscosity solutions for nonlinear elliptic partial differential equations 1 | ||
The theory of viscosity solutions was originally developed to understand 1st. order equations. Later, it was successfully extended to cover fully nonlinear 2nd. order elliptic and parabolic equations. This notion of solutions is surprisingly weak. Since candidates for solutions are just continuous functions. In fact, we only require that \"test\" polynomials (those who are tangent to the graph of u) satisfy the correct differential inequality (at the point of tangency). Very general existence results are combined with regularity theory to obtain a well developed and powerful tool to study a large class of PDE\'s. In these three talks, we\'ll focus on fully nonlinear elliptic equations, maximum principle, Harnack inequality and uniqueness (if time permits). | ||
| Note: WK short course | ||
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| Jorge Salazar (CMAF Lisboa, Univ. de Evora) | WPI seminar room | Thu, 21. Oct 04, 15:00 |
| Viscosity solutions for nonlinear elliptic partial differential equations 2 | ||
abstract: see Oct. 14 | ||
| Note: WK short course | ||
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| Jorge Salazar (CMAF Lisboa, Univ. de Evora) | WPI seminar room | Thu, 28. Oct 04, 15:00 |
| Viscosity solutions for nonlinear elliptic partial differential equations 3 | ||
abstract: see Oct. 14 | ||
| Note: WK short course | ||
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| Mikayelyan Hayk | WPI seminar room | Wed, 9. Feb 05, 15:00 |
| On the tangential touch between the free and the fixed boundaries for the two-phase obstacle-like problem | ||
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| Bandle Catherine | WPI seminar room | Mon, 14. Mar 05, 15:00 |
| Parabolic problems with dynamical boundary conditions and their spectral theory | ||
An existence theory for local solutions of a parabolic problem with time dependent boundary conditions is developed and a representation formula is given. It relies on the spectral theory of an associated elliptic problem with the eigenvalue parameter both in the equation and the boundary. The well-posedness depends on the direction of the boundary condition. We shall also discuss blowup phenomena in the presence of nonlinear sources. | ||
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| Vazquez Juan Luis | WPI seminar room | Mon, 14. Mar 05, 16:00 |
| The strange functional properties of the fast diffusion flow | ||
Fast diffusion flows generated by the equation $$ u_t=\\nabla\\cdot (u^{-n}\\nabla u)$$ with $n>0$, exhibit some peculiar nonlinear features for the functional analyst. We will report on problems of - strange existence, - extinction, - non uniqueness and - delayed regularity | ||
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