For one, the solutions often exhibit discontinuous derivatives across the free boundary, while they may be analytic in any neighborhood away from it.
12.
His recent research interests include nonlinear conservation laws, nonlinear waves, nonlinear equations of mixed type, free boundary problems, and geometric problems.
13.
His primary field of research is partial differential equations, with interests in stochastic processes, mathematical modeling, free boundary problems, and control theory.
14.
To solve the Stefan problem we not only have to solve the heat equation in each region, but we must also track the free boundary ?.
15.
Caffarelli received great recognition with his breakthrough paper " The regularity of free boundaries in higher dimensions " published in 1977 in " Acta Mathematica ".
16.
He was the first responsible ( jointly with Prof . J . F . Rodigues ) of the Programmes of Free Boundary Problems of the European Science Foundation.
17.
Where the Poisson problem corresponds to minimization of a quadratic functional over a linear subspace of functions, the free boundary problem corresponds to minimization over a convex set.
18.
The simplest case is that of two free boundaries, which Lord Rayleigh solved in 1916, obtaining Ra = & pi; 4 H " 657.51.
19.
In, 1D nonlinear Burger s equation with shock wave, shallow water equations for tide and current simulation, heat transfer problems, free boundary problems, and fractional diffusion equations.
20.
In 1971 he applied his mathematical methods to a free boundary problem in the filtration of liquids through porous media with applications in civil engineering ( by using the Baiocchi transform ).
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