heat equation for semi-infinite and infinite domainsThe use of Duhamel's theoremThe use of Green's function for solution of heat conductionThe use of the Laplace transformOne-dimensional composite mediumMoving heat source problemsPhase-change problemsApproximate analytic methodsIntegral-transform technique...
problems for heat equations and a class of deterministic evolution equations, respectively; some results on almost sure exponential stabilization of SPDEs were established in Caraballo et al. [3] by a Lyapunov function argument; stabilization by additive noise on solutions to semilinear parabolic SPD...
1InverseHeatConductionProblemsKrzysztofGrysaKielceUniversityofTechnologyPoland1.IntroductionIntheheatconductionproblemsiftheheatfluxand/ortemperaturehistoriesatthesurfaceofasolidbodyareknownasfunctionsoftime,thenthetemperaturedistributioncanbefound.Thisistermedasadirectproblem.Howeverinmanyheattransfersituations,thesurfaceheat...
Solutions of One Dimensional Heat Equation Using Excel WorksheetPeter Anthony
Properties of solutions of some control problems for a system described by the Navier-Stokes equations are studied with no restrictions on the control parameter. Necessary and sufficient conditions for an extremum are obtained, and the u... Fursikov,A V - Mathematics of the USSR-Sbornik 被引量...
Here also, problems are solved using the popular software, viz. “Mathcad”, “Engineering Equation Solver (EES)”, and MS EXCEL spreadsheet. Comments are included generously in the codes so that the logic behind the solutions is clear. ...
We develop a classification theory for the existence and non-existence of local in time solutions for initial value problems for nonlinear heat equations. By focusing on some quasi-scaling property and its invariant integral, we reveal the explicit threshold integrability of initial data that classifie...
In this paper, we consider a stochastic heat equation with multiplicative bi-fractional Brownian sheet. Using the technique of Feynman-Kac formula and Malliavin calculus, we give an explicit formula of the weak solution and study the regularity.
Carmona and Y. Hu. We also get slightly improved bounds on the lower tail of the solutions of the stochastic heat equation started with a delta initial condition.关键词: Stochastic heat equation directed polymers in random environments Kardar-Parisi-Zhang equation ...
The mathematical model for this situation is a heat equation in two-dimensions with a nonlinear source term, which is localized around a reference point that is allowed to move. Results are derived that indicate the roles played by the size, strength and motion of the localized source in ...