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MSC 2010: 26A33, 33E12, 34K29, 34L15, 35K57, 35R30We prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.
We study the existence and the uniqueness of the weak solution of an inverse problem for a semilinear higher order ultraparabolic equation with Lipschitz nonlinearity. The main aim is to determine the weak solution of the equation and some functions that depend on the time variable, appearing on the right-hand side of the equation. The overdetermination conditions introduced are of integral type. In order to prove the solvability of this problem in Sobolev spaces we use the Galerkin method and the...
We study a microfluidic flow model where the movement of several charged species is coupled with electric field and the motion of ambient fluid. The main numerical difficulty in this model is the net charge neutrality assumption which makes the system essentially overdetermined. Hence we propose to use the involutive and the associated augmented form of the system in numerical computations. Numerical experiments on electrophoresis and stacking show that the completed system significantly improves...
We study a microfluidic flow model where the movement of several charged species is
coupled with electric field and the motion of ambient fluid. The main numerical difficulty in this model is the net charge neutrality
assumption which makes the system essentially overdetermined. Hence we propose to use the involutive and the associated augmented form
of the system in numerical computations. Numerical experiments on electrophoresis and stacking show that the completed system significantly improves...
In this contribution we add a unilateral term to the Thomas model and investigate the resulting Turing patterns. We show that the unilateral term yields nonsymmetric and irregular patterns. This contrasts with the approximately symmetric and regular patterns of the classical Thomas model. In addition, the unilateral term yields Turing patterns even for smaller ratio of diffusion constants. These conclusions accord with the recent findings about the influence of the unilateral term in a model for...
We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution , the graph of its blow-up points and the set of all characteristic points and show that is locally finite. Finally, given , we show that in selfsimilar variables, the solution decomposes into a decoupled sum of (at least two) solitons, with alternate signs and that forms a...
In Hörmander inner product spaces, we investigate initial-boundary value problems for an arbitrary second order parabolic partial differential equation and the Dirichlet or a general first-order boundary conditions. We prove that the operators corresponding to these problems are isomorphisms between appropriate Hörmander spaces. The regularity of the functions which form these spaces is characterized by a pair of number parameters and a function parameter varying regularly at infinity in the sense...
This paper is concerned with iterative methods for parabolic functional differential equations with initial boundary conditions. Monotone iterative methods are discussed. We prove a theorem on the existence of solutions for a parabolic problem whose right-hand side admits a Jordan type decomposition with respect to the function variable. It is shown that there exist Newton sequences which converge to the solution of the initial problem. Differential equations with deviated variables and differential...
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