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This paper gives a new and short proof of existence and uniqueness of the Polubarinova-Galin equation. The existence proof is an application of the main theorem in Lins paper. Furthermore, we can conclude that every strong solution can be approximated by many strong polynomial solutions locally in time.
This paper addresses a rescaling behavior of some classes of global solutions to the zero surface tension Hele-Shaw problem with injection at the origin, ${Omega(t)}_{tgeq 0}$. Here $Omega(0)$ is a small perturbation of $f(B_{1}(0),0)$ if $f(xi,t)$ i
We use a new method to prove uniqueness theorem for a coefficient inverse scattering problem without the phase information for the 3-D Helmholtz equation. We consider the case when only the modulus of the scattered wave field is measured and the phas
We aim this paper to develop the classical lattice models with unbounded spin to the case of non-quadratic polynomial interaction. We demonstrate that the distinct relation between the growths of potentials leads to the uniqueness and the fast decay of correlations for Gibbs measure.
Consider a non-relativistic quantum particle with wave function inside a region $Omegasubset mathbb{R}^3$, and suppose that detectors are placed along the boundary $partial Omega$. The question how to compute the probability distribution of the time
We show that Tsirelsons problem concerning the set of quantum correlations and Connes embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchbergs QWEP conjecture) are essentially equivalent. Specifically,