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On a system of equations of evolution with a non-symmetrical parabolic part occuring in the analysis of moisture and heat transfer in porous media

Jiří Vala (2002)

Applications of Mathematics

Most non-trivial existence and convergence results for systems of partial differential equations of evolution exclude or avoid the case of a non-symmetrical parabolic part. Therefore such systems, generated by the physical analysis of the processes of transfer of heat and moisture in porous media, cannot be analyzed easily using the standard results on the convergence of Rothe sequences (e.g. those of W. Jäger and J. Kačur). In this paper the general variational formulation of the corresponding...

On Borel summable solutions of the multidimensional heat equation

Sławomir Michalik (2012)

Annales Polonici Mathematici

We give a new characterisation of Borel summability of formal power series solutions to the n-dimensional heat equation in terms of holomorphic properties of the integral means of the Cauchy data. We also derive the Borel sum for the summable formal solutions.

On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations

Jérôme Le Rousseau, Gilles Lebeau (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Local and global Carleman estimates play a central role in the study of some partial differential equations regarding questions such as unique continuation and controllability. We survey and prove such estimates in the case of elliptic and parabolic operators by means of semi-classical microlocal techniques. Optimality results for these estimates and some of their consequences are presented. We point out the connexion of these optimality results to the local phase-space geometry after conjugation...

On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations∗∗∗

Jérôme Le Rousseau, Gilles Lebeau (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Local and global Carleman estimates play a central role in the study of some partial differential equations regarding questions such as unique continuation and controllability. We survey and prove such estimates in the case of elliptic and parabolic operators by means of semi-classical microlocal techniques. Optimality results for these estimates and some of their consequences are presented. We point out the connexion of these optimality results to the local phase-space geometry after conjugation...

On coupled thermoelastic vibration of geometrically nonlinear thin plates satisfying generalized mechanical and thermal conditions on the boundary and on the surface

Hans-Ullrich Wenk (1982)

Aplikace matematiky

The vibration problem in two variables is derived from the spatial situation (a plate as a three-dimensional body) on the basis of geometrically nonlinear plate theory (using Kármán's hypothesis) and coupled linear thermoelasticity. That leads to coupled strongly nonlinear two-dimensional equilibrium and heat conducting equations (under classical mechanical and thermal boundary conditions). For the generalized problem with subgradient conditions on the boundary and in the domain (including also...

On Gaussian Brunn-Minkowski inequalities

Franck Barthe, Nolwen Huet (2009)

Studia Mathematica

We are interested in Gaussian versions of the classical Brunn-Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrhard inequality for m Borel or convex sets based on a previous work by Borell. Our method also yields semigroup proofs of the geometric Brascamp-Lieb inequality and of its reverse form, which follow exactly the same lines.

On rates of propagation for Burgers’ equation

William Alan Day, Giuseppe Saccomandi (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We give asymptotic formulae for the propagation of an initial disturbance of the Burgers’ equation.

Currently displaying 221 – 240 of 398