heat equations
Some optimal control problems of heat equations with weighted controls
... timization is to improve a variable in order to maximize a benefit (or minimize a cost). The time and norm optimal control problems are important and interesting branches of opti- mization. For the deterministic systems, ...
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An approximation result for a class of stochastic heat equations with colored noise
... and infinity by a constant profile if we are interested in studying the large-time or large-space asymptotics for the equation; see for instance [8] and [9]. See also the recent preprint [5] which deals with comparison ...
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Numerical Quenching for Heat Equations with Coupled Nonlinear Boundary Flux
... reactions, heat transfer, etc, where u and v represent the temperatures of two different materials during heat ...of heat equations system with nonlinear boundary conditions has been the ...
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Temporal variation for fractional heat equations with additive white noise
... moreover, the process t → u(t, x) has a nontrivial quartic variation. As a general conclu- sion from these results, in Sun et al. [] we considered the quadratic covariations and Itô’s formula for the solution. The above ...
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Multiplicative stochastic heat equations on the whole space
... stochastic heat equations on unbounded domains. The two main equations our result covers are, on the one hand the parabolic Anderson model on R 3 , and on the other hand the KPZ equation on R via the ...
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On some properties of a class of fractional stochastic heat equations
... The above assumptions on σ are quite natural and have been used in various works; see [10,11]. The lower bound is essentially a growth condition which is needed for our results. These inequalities also imply that σ(0) = ...
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Quantitative unique continuation for the linear coupled heat equations
... parabolic equations was derived in in the literature ...parabolic equations with time independent co- efficients in terms of the eigenfunctions of the corresponding elliptic operator, and their results ...
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Quantitative unique continuation for the heat equations with inverse square potential
... parabolic equations was derived in 1974 in ...parabolic equations with time independent coefficients by the properties of eigenfunctions of the corresponding elliptic operator, and this approach cannot be ap- ...
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Moment bounds for a class of fractional stochastic heat equations
... which gives the required exponential bound. For t > T , (3.1) together with Proposition 2.6 gives the required bound with the correct rate with respect of λ. We have thus given two different ways of proving ...
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An application of Lauricella hypergeometric functions to the generalized heat equations
... fractional heat conduction equation is studied by Povstenko in 2004 ...the heat conduction equation with a time-fractional ...the heat conduction with time and space fractional derivatives and on the ...
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Blow-up for nonlinear heat equations with absorptions
... parabolic equations with heat sources have been studied by many authors, and the reader is referred to [ 3-5, 9, 11, 14 ] and the references ...parabolic equations with no sources, some necessary ...
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Controllability and constrained controllability for nonlocal Hilfer fractional differential systems with Clarke’s subdifferential
... differential equations can be observed in many areas such as population dynamics, heat conduction in materials with memory, seepage flow in porous media, autonomous mobile robots, fluid dynamics, traffic models, ...
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Numeric modeling method usage for heat conductivity equations solution
... And so this work aim is the following. Let’s calculating the known test problem, given in the work [12], for a sweep method applicability check to solve non-stationary one-dimensional differential heat ...
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The Compressible Navier Stokes Equations with Weak Viscosity and Heat Conductivity
... and heat conductivity involve the Knudsen number, it is quite hard to establish the higher regularities of the ...differential equations which cannot be available ...and heat conductivity in a ...
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An open source toolbox for PEM fuel cell simulation
... The distribution of hydrogen and oxygen mass fractions are shown in Figure 10a,b, respectively. The consumption of the reactant gases by the electrochemical reaction leads to a decrease in their mass fractions going from ...
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Effect of the Air Channel Depth on the Efficiency of Photovoltaic/Thermal Sensor with a Parabolic Concentrator
... extract heat from the panel, thereby cooling the cells and hence increasing their ...balance equations of the whole system are computed using the GAUSS-SAIDEL method, allowing to estimate heat ...
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A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time Dependent Coefficient
... In our knowledge, there have been many papers on the linear homogeneous case of the backward problem, but there are a few papers on the nonhomogeneous case and the nonlin- ear case such as 1–6; especially, the nonlinear ...
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Development and Verification of Accretion Similarity Conversion Method for Gas Bottom Blowing Process inside Pyrometallurgical Vessels
... the heat states of the liquid matter to the point of being solidified between two units are similar, their Stefan Numbers are set to be identical and liquid temperature when solid accretion can be formed in the hot ...
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STABILITY INEQUALITIES FOR THE DELAY PSEUDO$-$PARABOLIC EQUATIONS
... above equations are usually called Sobolev type or pseudo- parabolic equations, which appear in engineering fields, such as, for instance, flows of fluids through fissured rock, heat condition ...
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Mathematical Analysis of Solar Still With Storage
... Energy balance equation are used for the modelling of solar still with storage. The equation are made for each point on solar still i.e. glass, water, basin and storage. After solving these equations using ...
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