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Sticky Brownian Motions and a Probabilistic Solution to a Two-Point Boundary Value Problem
In this paper, we study a two-point boundary value problem consisting of the heat equation on the open interval (0,1) with boundary conditions which...
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Heat Transfer in a Complex Medium
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of...
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Quasi-Maximum Modulus Principle for the Stokes Equations
In this paper, we extend the maximum modulus estimate of the solutions of the nonstationary Stokes equations in the bounded C 2 cylinders for the...
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Radon Measure-Valued Solutions for a Class of Quasilinear Parabolic Equations
Initial value problems for quasilinear parabolic equations having Radon measures as initial data have been widely investigated, looking for solutions...
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On the Boundary Value Problem for p-parabolic Equations
We derive a fundamental existence theorem for the equation $$ u'_t (x,t) -...
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Vorticity and Regularity for Viscous Incompressible Flows under the Dirichlet Boundary Condition. Results and Related Open Problems
In reference [7] it is proved that the solution of the evolution Navier–Stokes equations in the whole of R 3 must be smooth if the direction of the...
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Local Exact Controllability of Micropolar Fluids
This paper is devoted to prove the local exact controllability to the trajectories of micropolar fluids with distributed controls supported in small...
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Heat Kernel Asymptotics of Zaremba Boundary Value Problem
The Zaremba boundary-value problem is a boundary value problem for Laplace-type second-order partial differential operators acting on smooth sections...