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37 results on '"Kersner, Robert"'

2. Heat conduction: hyperbolic self-similar shock-waves in solids

Author

Barna, Imre Ferenc and Kersner, Robert

Subjects
Mathematical Physics
Abstract

Analytic solutions for cylindrical thermal waves in solid medium is given based on the nonlinear hyperbolic system of heat flux relaxation and energy conservation equations. The Fourier-Cattaneo phenomenological law is generalized where the relaxation time and heat propagation coefficient have a general power law temperature dependence. From such laws one cannot form a second order parabolic or telegraph-type equation. We consider the original non-linear hyperbolic system itself with the self-similar Ansatz for the temperature distribution and for the heat flux. As results continuous and shock-wave solutions are presented. For physical establishment numerous materials with various temperature dependent heat conduction coefficients are mentioned., Comment: 5 pages, 2 figures, the manuscript is submitted to Eur. Phys. Letters

Published
2012
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3. Heat conduction: a telegraph-type model with self-similar behavior of solutions

Author

Barna, Imre Ferenc and Kersner, Robert

Subjects
Mathematical Physics
Abstract

For heat flux $q$ and temperature $T$ we introduce a modified Fourier--Cattaneo law $q_t+ l \frac{q}{t}= - kT_x .$ The consequence of it is a non-autonomous telegraph-type equation. % $\epsilon S_{tt} + \frac{a}{t} S_t = S_{xx}$ . This model already has a typical self-similar solution which may be written as product of two travelling waves modulo a time-dependent factor and might play a role of intermediate asymptotics., Comment: 5 Pages, 2 Figures, it will be submitted to Physical Review

Published
2010

5. Reaction-diffusion

Author

Gilding, Brian H., Kersner, Robert, Brezis, Haim, editor, Gilding, Brian H., editor, and Kersner, Robert, editor

Published
2004
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6. Power-law equations

Author

Gilding, Brian H., Kersner, Robert, Brezis, Haim, editor, Gilding, Brian H., editor, and Kersner, Robert, editor

Published
2004
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7. Wavefronts

Author

Gilding, Brian H., Kersner, Robert, Brezis, Haim, editor, Gilding, Brian H., editor, and Kersner, Robert, editor

Published
2004
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8. Convection-diffusion

Author

Gilding, Brian H., Kersner, Robert, Brezis, Haim, editor, Gilding, Brian H., editor, and Kersner, Robert, editor

Published
2004
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9. Transformations

Author

Gilding, Brian H., Kersner, Robert, Brezis, Haim, editor, Gilding, Brian H., editor, and Kersner, Robert, editor

Published
2004
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10. Travelling waves

Author

Gilding, Brian H., Kersner, Robert, Brezis, Haim, editor, Gilding, Brian H., editor, and Kersner, Robert, editor

Published
2004
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11. General theory

Author

Gilding, Brian H., Kersner, Robert, Brezis, Haim, editor, Gilding, Brian H., editor, and Kersner, Robert, editor

Published
2004
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12. Introduction

Author

Gilding, Brian H., Kersner, Robert, Brezis, Haim, editor, Gilding, Brian H., editor, and Kersner, Robert, editor

Published
2004
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13. Unbounded waves

Author

Gilding, Brian H., Kersner, Robert, Brezis, Haim, editor, Gilding, Brian H., editor, and Kersner, Robert, editor

Published
2004
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23. Discontinuous limit semigroups for the singular Zhang equation and its hydrodynamic version

Author

Galaktionov, Victor A. and Kersner, Robert

Subjects
Applied Mathematics, 35K55, Mathematics::Analysis of PDEs, 35K65, Analysis
Abstract

We study properties of the solutions of two semilinear parabolic equations, the singular Zhang equation and its hydrodynamic version, $$ u_t=u_{xx}+\ln|u_x|\quad {\rm and} \,\,\,v_t = v_{xx} + {v_x}/v , $$ which exhibit strong singularities on the sets $\{u_x=0\}$ and $\{v = 0\}$ respectively. Using the concept of maximal solutions constructed by a regular monotone approximation, we prove existence and boundedness of such solutions. We show that for some classes of initial data, the solutions become instantly entirely singular: $v(t) \equiv 0$ and $u(t)\equiv -\infty$ for any arbitrarily small $t>0$. In general, we establish that for both equations the solutions cannot satisfy the initial condition in any weak sense; i.e., the corresponding semigroups are not continuous at $t=0$. Such discontinuous semigroups are exhibited by a wide class of singular nonlinear parabolic equations.

Published
2001

31. On a Stefan-type model arising in ecology

Author

Berezovsky, Arnold, Kersner, Robert, and Peletier, Bert

Subjects
*CHEMICAL processes, *CHEMICALS, *MATHEMATICAL physics, *EQUATIONS
Abstract

Abstract: We discuss the dispersal of a chemical, emitted from a point source, into a reacting medium. The diffusion and reaction are such that a front emerges, so that at all times the chemical remains confined to a bounded domain around the source. We focus on the final stationary state which is a non-standard Stefan-type boundary value problem for an Emden–Fowler equation. We prove its existence and uniqueness and obtain, analytically as well as numerically, bounds for the location of the front and for the concentration profile. [Copyright &y& Elsevier]

Published
2006
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36. The Cauchy problem for <f>ut=Δu+&z.sfnc;∇u&z.sfnc;q</f>

Author

Gilding, Brian H., Guedda, Mohammed, and Kersner, Robert

Subjects
*REAL numbers, *NONLINEAR differential equations, *MATHEMATICS
Abstract

With q a positive real number, the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces. In that context it is known as the generalized deterministic KPZ equation. The paper is concerned with the initial-value problem for the equation under the assumption that the initial-data function is bounded and continuous. Results on the existence, uniqueness, and regularity of solutions are obtained. [Copyright &y& Elsevier]

Published
2003
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37. Lid speculum works nasally, temporarily.

Author

Kersner, Robert M.

Subjects
*OPHTHALMOLOGY equipment
Abstract

Introduces the Reversible Eyelid Speculum from Rhein Medical Inc. Description of outdated eyelid specula; Instrument's features; Advantages for the surgery and the surgeon.

Published
1997

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