Noemi Wolanski

Blow up results and localization of blow up points for the heat equation with a nonlinear boundary condition

Abstract In this paper we study the large time behavior of positive solutions of the heat equation under the nonlinear boundary condition ∂u ∂ν = f(u) , where η is the outward normal and f is nondecreasing with f(u) > 0 for u > 0. We show that if Ω = B R and 1/f is integrable at infinity there is finite time blow up for any initial datum. In the two dimensional case we show that this is true for any smooth simply connected domain. In the radially symmetric case if f ϵ C2 is convex and satisfies the properties above we show that blow up occurs only at the boundary.

Global behavior of positive solutions to nonlinear diffusion problems with nonlinear absorption through the boundary

The author studies the global behavior of positive solutions to

Blow-up vs. global existence for a semilinear reaction-diffusion system in a bounded domain

u_t = Delta phi (u)

Uniqueness of solution to a free boundary problem from combustion

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Regularity of the Free Boundary in an Optimization Problem Related to the Best Sobolev Trace Constant

B_R times (0,T);{{delta phi (u)} / {delta nu = f(u)}}

A finite element method for the Mindlin-Reissner plate model

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Singular Perturbation in a Nonlocal Diffusion Problem

S_R times (0,T)

A SINGULAR PERTURBATION PROBLEM FOR A QUASI-LINEAR OPERATOR SATISFYING THE NATURAL GROWTH CONDITION OF LIEBERMAN

; and

ASYMPTOTIC BEHAVIOR FOR A NONLOCAL DIFFUSION EQUATION WITH ABSORPTION AND NONINTEGRABLE INITIAL DATA. THE SUPERCRITICAL CASE

u(x,0) = u_0 (x)

A free-boundary problem in combustion theory

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