Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Strong solutions to a parabolic equation with linear growth with respect to the gradient variable
2018
Abstract In this paper we prove existence and uniqueness of strong solutions to the homogeneous Neumann problem associated to a parabolic equation with linear growth with respect to the gradient variable. This equation is a generalization of the time-dependent minimal surface equation. Existence and regularity in time of the solution is proved by means of a suitable pseudoparabolic relaxed approximation of the equation and a passage to the limit.
Comparison of perceptually uniform quantisation with average error minimisation in image transform coding
1999
An alternative transform coder design criterion based on restricting the maximum perceptual error of each coefficient is proposed. This perceptually uniform quantisation of the transform domain ensures that the perceptual error will be below a certain limit regardless of the particular input image. The results show that the proposed criterion improves the subjective quality of the conventional average error criterion even if it is weighted with the same perceptual metric.
Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian
2004
AbstractThis paper deals with two mixed nonlinear boundary value problems depending on a parameter λ. For each of them we prove the existence of at least three generalized solutions when λ lies in an exactly determined open interval. Usefulness of this information on the interval is then emphasized by means of some consequences. Our main tool is a very recent three critical points theorem stated in [Topol. Methods Nonlinear Anal. 22 (2003) 93–104].
On the moving load problem in Euler–Bernoulli uniform beams with viscoelastic supports and joints
2016
This paper concerns the vibration response under moving loads of Euler–Bernoulli uniform beams with translational supports and rotational joints, featuring Kelvin–Voigt viscoelastic behaviour. Using the theory of generalized functions to handle the discontinuities of the response variables at the support/joint locations, exact beam modes are obtained from a characteristic equation built as determinant of a (Formula presented.) matrix, for any number of supports/joints. Based on pertinent orthogonality conditions for the deflection modes, the response under moving loads is built in the time domain by modal superposition. Remarkably, all response variables are built in a closed analytical for…
Estimation of the mean crystal size and the moments of the crystal size distribution in batch crystallization processes
2016
International audience; A cascade high gain observer is designed to estimate the first four leading moments of the crystal size distribution (CSD) and the mean crystal size in batch crystallization processes. The proposed observer is based on a well-known transformation of the partial differential equation describing the CSD to a set of ordinary differential equations (the method of moments). Due to numerical difficulties resulting from the important differences in the magnitudes of the moments, a set of new variables is computed to allow a good estimation of the moments and thus the mean crystal size. In this work, only solute concentration and crystallizer temperature are used to estimate…
An alternative formulation of the boundary element method
1982
Abstract The paper suggests an alternative formulation of the Boundary Element Method, in which singular solutions generated by unit dislocations are required and moreover the stresses at the interior points of the body are directly computed from the boundary quantities, without passing through the displacements. Relationships between the singular solutions for unit dislocation and unit force are derived.
On Fourier integral operators with Hölder-continuous phase
2018
We study continuity properties in Lebesgue spaces for a class of Fourier integral operators arising in the study of the Boltzmann equation. The phase has a H\"older-type singularity at the origin. We prove boundedness in $L^1$ with a precise loss of decay depending on the H\"older exponent, and we show by counterexamples that a loss occurs even in the case of smooth phases. The results can be seen as a quantitative version of the Beurling-Helson theorem for changes of variables with a H\"older singularity at the origin. The continuity in $L^2$ is studied as well by providing sufficient conditions and relevant counterexamples. The proofs rely on techniques from Time-frequency Analysis.
On the definition of viscosity solutions for parabolic equations
2001
In this short note we suggest a refinement for the definition of viscosity solutions for parabolic equations. The new version of the definition is equivalent to the usual one and it better adapts to the properties of parabolic equations. The basic idea is to determine the admissibility of a test function based on its behavior prior to the given moment of time and ignore what happens at times after that.
Local moment problem
2014
The work is devoted to the local moment problem, which consists in finding of non-decreasing functions on the real axis having given first 2n + 1, n ≥ 0, power moments on the whole axis and also 2m + 1 first power moments on a certain finite axis interval. Considering the local moment problem as a combination of the Hausdorff and Hamburger truncated moment problems we obtain the conditions of its solvability and describe the class of its solutions with minimal number of growth points if the problem is solvable. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
Stable moment mappings and singular lagrangian Fibrations
2005
We study singular Lagrangian fibrations given by moment mappings using cohomological methods. We give a theorem for the stability of these foliations and construct a symplectic version of Mather’s stable mapping theorem.