相关论文: The Heaviside equation for laser heating of the fu…
In his paper the two mode Heaviside equation was formulated and solved. It was shown that the interaction of ultra-short laser pulses with matter leads to two mode excitation electrons and phonons which afterwards diffuse with finite…
We report studies of the solution of the Heaviside - Klein - Gordon thermal equation. As the result it is shown that the solution consists of two components: the fast thermal wave and slow diffusion for very large (compared to relaxation…
In this paper we obtain necessary conditions on the initial value for the solvability of the Cauchy problem for semilinear heat equations. These necessary conditions were already obtained in the framework of integral solutions, but not in…
In this paper the attosecond laser pulse tissue is investigated. The master equation is formulated and solved. The thermal relaxation time and thermal waves speed are calculated
We introduce and study an extension of the heat equation relevant to relativistic energy formula involving square root of differential operators. We furnish exact solutions of corresponding Cauchy (initial) problem using the operator…
We consider two high-frequency thermal processes in uniformly heated harmonic crystals relaxing towards equilibrium: (i) equilibration of kinetic and potential energies and (ii) redistribution of energy among spatial directions. Equation…
We consider the Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity. We establish local well-posedness result in Orlicz spaces. We derive the existence of global solutions for small initial data. We…
In this paper the interaction of ultrashort laser pulses with matter is investigated. The scattering and potential motion of heat carriers, as well as the external force are considered. It is shown that the heat transport is described by…
This paper considerers the problem of computing the value of a solution of the heat equation at a given point inside a bounded domain after the initial time. It is assumed that the initial value of the solution inside the domain (possibly…
We study the linear heat equation on a halfspace with a linear dynamical boundary condition. We are interested in an appropriate choice of the function space of initial functions such that the problem possesses a solution. It was known…
In this paper the continuous laser beam interaction with matter is investigated. The velocities of the thermal propagation are calculated. It is shown that for the value of the product, omega x tau>1, omega is the angular frequency of the…
In this paper the existence of the thermal tachyons i.e. quanta of temperature field, with is described in the theoretical frame of hyperbolic thermal equation. The modified Lorentz transformation are developed. It is argued that thermal…
We obtain necessary conditions and sufficient conditions on the existence of solutions to the Cauchy problem for a fractional semilinear heat equation with an inhomogeneous term. We identify the strongest spatial singularity of the…
In most systems, thermal diffusion is intrinsically slow with respect to mechanical relaxation. We devise here a generic approach to accelerate the relaxation of the temperature field of a 1D object, in order to beat the mechanical time…
Specific heat and linear thermal expansivity are fundamental thermal dynamics and have been proven as interesting relaxing quantities to investigate in glass transition and glassy state. However, their possibility has much less been…
We consider the weak solutions to the Euler-Fourier system describing the motion of a compressible heat conducting gas. Employing the method of convex integration, we show that the problem admits infinitely many global-in-time weak…
In this paper the Boltzmann transport equation for thermal processes induced by ultra-short laser pulses is formulated and solved. For thermal process where the duration of the laser pulse (femtoseconds - attoseconds) is shorter than the…
We obtain necessary conditions and sufficient conditions for the solvability of the heat equation in a half-space of ${\bf R}^N$ with a nonlinear boundary condition. Furthermore, we study the relationship between the life span of the…
In this paper laser heating of human cornea is investigated. The new heat transport equation in cornea -hyperbolic Pennes equation is formulated and solved. It is shown that for ultra-short laser pulses the thermal energy propagates with…
The paper is concerned with the Cauchy problem for a semi-linear hyperdissipative heat equation in Besov and Triebel-Lizorkin spaces which is related to the generalized Gauss-Weierstrass semi-group via Duhamel's principle. Using caloric…