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Translating solutions to the second boundary value problem for curvature flows
We consider the flow of strictly convex hypersurfaces driven by curvature functions subject to the second boundary condition and show that they...
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Asymptotic Behaviour and Global Existence of Solutions for Some Classes of Nonlinear Parabolic Equations
The paper deals with the asymptotic behaviour and global existence of solutions for some classes of nonlinear parabolic equations in regard to the...
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Dirichlet Boundary Control of Semilinear Parabolic Equations Part 1: Problems with No State Constraints
This paper is concerned with distributed and Dirichlet boundary controls of semilinear parabolic equations, in the presence of pointwise state...
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Dirichlet Boundary Control of Semilinear Parabolic Equations Part 2: Problems with Pointwise State Constraints
This paper is the continuation of the paper ``Dirichlet boundary control of semilinear parabolic equations. Part 1: Problems with no state...
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The nonsymmetric case of the Keller-Segel model in chemotaxis: some recent results
Looking at the nonsymmetric case of a reaction-diffusion model known as the Keller-Segel model, we summarize known facts concerning (global in time)...
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Galerkin proper orthogonal decomposition methods for parabolic problems
In this work error estimates for Galerkin proper orthogonal decomposition (POD) methods for linear and certain non-linear parabolic systems are...
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Time-dependent parabolic problems on non-cylindrical domains with inhomogeneous boundary conditions
We study the relationship between the Dirichlet problem and the Cauchy problem with inhomogeneous boundary conditions for local operators. Our...
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Numerical Techniques for the Recovery of an Unknown Dirichlet Data Function in Semilinear Parabolic Problems with Nonstandard Boundary Conditions
We study a semilinear parabolic partial differential equation of second order in a bounded domain Ω ⊂ ℝN, with nonstandard boundary conditions (BCs)...
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Oblique derivative problem for parabolic operators with VMO coefficients
Let Q T be a cylinder in R n × R + of height T >0 with C 1,1 smooth base Ω and lateral boundary S T . Unique strong solvability in Sobolev spaces W ...
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The attractors of partial differential equations
In this paper the reaction-diffusion systems and the damped wave systems with non-linear terms of gradient form are studied, and the conditions for...
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Homogenization of a boundary condition for the heat equation
An asymptotic analysis is given for the heat equation with mixed boundary conditions rapidly oscillating between Dirichlet and Neumann type. We try...
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Initial-Mixed Boundary Value Problems for Parabolic Equations of Second Order with Measurable Coefficients in a Higher Dimensional Domain
In [1], Yu. A. Alkhutov and I. T. Mamedov discussed the solvability of the Dirichlet problem for a linear nondivergence uniformly parabolic equations...
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Comment on ‘Pricing double barrier options using Laplace transforms’ by Antoon Pelsser
In this paper we comment on the paper “Pricing Double Barrier Options using Laplace Transforms” by Antoon Pelsser. We illustrate that the same...
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Absence de la L∞-contractivité pour les semi-groupes associés aux opérateurs elliptiques complexes sous forme divergence
Soit un opérateur elliptique du second ordre à coefficients complexes sur un ouvert de ℝ N . On obtient des conditions nécessaires et suffisantes sur...
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The Oblique Derivative Problem for Nonlinear Parabolic Equations of Second Order with Measurable Coefficients in a Higher Dimensional Domain
In [1], Yu. A. Alkhutov and I. T. Mamedov discussed the solvability of the Dirichlet problem for linear uniformly parabolic equations...
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Criteria for Validity of the Maximum Norm Principle for Parabolic Systems
We consider systems of partial differential equations, which contain only second derivatives in the x variables and which are uniformly parabolic in...
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Initial-Irregular Oblique Derivative Problems for Nonlinear Parabolic Complex Equations of Second Order with Measurable Coefficients
This paper deals with initial-irregular oblique derivative boundary value problems for nonlinear and nondivergence parabolic complex equations of...
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Smoothing properties of transition semigroups relative to SDEs with values in Banach spaces
In the present paper we consider the transition semigroup P t related to some stochastic reaction-diffusion equations with the nonlinear term f ...