Degenerate heat equation

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August undefined, 2024

WebDec 13, 2014 · However, only few of them are concerned with degenerate heat equations. In this work, we consider an inverse problem of identifying the source coefficient in a … WebAbstract. We prove null controllability results for the degenerate one-dimensional heat equation u t − (x αu x) x = fχ ω,x∈ (0,1),t∈ (0,T). As a consequence, we obtain null …

The cost of controlling weakly degenerate parabolic equations by ...

WebAbstract. We prove null controllability results for the degenerate one-dimensional heat equation u t − (x αu x) x = fχ ω,x∈ (0,1),t∈ (0,T). As a consequence, we obtain null controllability results for a Crocco-type equation that describes the velocity ﬁeld of a laminar ﬂow on a ﬂat plate. 1. Introduction Web3 NONHOMOGENEOUS DEGENERATE/SINGULAR EQUATION In this section, we prove the null controllability for the following nonhomogeneous, degenerate, singular heat equations using a new modified Carleman inequality. This null controllability results will be the key tool for the controllability of the initial problems (5) and (6). bus times in crawley

Carleman Estimates for a Class of Degenerate Parabolic Operators

Webdegenerate equation and its fundamental solution. when a ( x, t) ≥ a 0 > 0. In fact, if write the fundamental solution for that (i.e. the Green's function) in the special case of a ( x, t) … WebNov 5, 2024 · Abstract In this paper, we study the inverse problem of identifying the initial value of a two-dimensional degenerate parabolic equation, which often appears in the fields of engineering, physics, and computer image processing. Firstly, the difference scheme of forward problem is established by using the finite volume method. WebJul 15, 2024 · In this paper, we investigate the stability of a degenerate heat equation ut(x,t)=(xαux(x,t))x,x∈(0,1),t>0in a non-cylindrical/cylindrical domain. It is well known that the heat equation... cch real estate professional election

3.3: Degenerate Fermi gas - Physics LibreTexts

Null controllability of degenerate heat equations - Project Euclid

WebFeb 7, 2024 · A semi-infinite inverse source problem in heat conduction equations is considered, where the source term is assumed to be compactly supported in the region. After introducing a suitable artificial boundary, the semi-infinite problem is transformed into a bounded one and the corresponding exact expression of the boundary … WebGiven α ∈ [ 0, 2) and f ∈ L 2 ( ( 0, T) × ( 0, 1)), we derive new Carleman estimates for the degenerate parabolic problem w t + ( x α w x) x = f, where ( t, x) ∈ ( 0, T) × ( 0, 1), associated to the boundary conditions w ( t, 1) = 0 and w ( t, 0) = 0 if 0 ≤ α < 1 or ( x α w x) ( t, 0) = 0 if 1 ≤ α < 2. bus times in grimsbyWebNov 10, 2001 · Using a new method, we generalize the blow up and existence result from P. Baras and J. A. Goldstein (1984, Trans. Amer. Math. Soc.284, 121–139) to heat … bus times in gosport

"WebAug 30, 2024 · There is a rich literature on such a degenerate diffusion in the case of $\alpha=1$. Our work extends part of the existing results to cases with more general … " - Degenerate heat equation

Degenerate heat equation

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WebDegenerate is used in quantum mechanics to mean 'of equal energy.'. It usually refers to electron energy levels or sublevels. For example, orbitals in the 2p sublevel are degenerate - in other words the 2p x, 2p y, and 2p z … WebJul 15, 2024 · This phenomenon coincides with that in [13] for the degenerate heat equation in non-cylindrical domain (linear moving boundary) where the decay rate is …

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WebDegenerate Heat Equation M. J. Huntul1 and D. Lesnic2,* Abstract: In this paper, we consider solving numerically for the ﬁrst time inverse problems of determining the time-dependent thermal diffusivity coefﬁcient for a weakly degenerate heat equation, which vanishes at the initial moment of time, and/or the convection WebThe existence and non-existence of global solutions and the L p blow-up of non-global solutions to the initial value problem u′ ( t )=Δ u ( t )+ u ( t) γ on R n are studied. We consider only γ >1. In the case n ( γ − 1)/2=1, we present a simple proof that there are no non-trivial global non-negative solutions.

WebThe equation v t a v x is uniformly parabolic, and has a unique solution v such that v ( x, 0) = u 0 ( x) (this way you do not have to worry about boundary values at x = ϵ .) Now you would like to prove that v ϵ (or a subsequence) converges in some sense to a solution u of the original problem. WebJul 8, 2024 · In this paper, we recover the boundary null controllability for the degenerate heat equation by analyzing the asymptotic behavior of an eligible family of state-control …

WebFeb 19, 2024 · The heat equation for a general volume form that not necessarily coincides with the Riemannian one is useful in sub-Riemannian geometry, where a canonical volume only exists in certain cases. ... was observed first by Souriau that the coadjoint orbits carry a natural symplectic structure and there is a closed non-degenerate G-invariant 2-form ... WebA regularization method is used to study the equation and several useful estimates are obtained. The main This paper studies a fourth-order, nonlinear, doubly-degenerate parabolic equation derived from the thin film equation in spherical geometry.

WebFeb 1, 2005 · In this section, we prove the null controllability for the following nonhomogeneous, degenerate, singular heat equations using a new modified …

WebIn this paper, we investigate the stability of a degenerate heat equation ut(x,t)=(xαux(x,t))x,x∈(0,1),t>0in a non-cylindrical/cylindrical domain. bus times inverkip to greenockWebA regularization method is used to study the equation and several useful estimates are obtained. The main This paper studies a fourth-order, nonlinear, doubly-degenerate … bus times inverkeithing to edinburghWebIn this paper, we study the null controllability and approximate controllability for a class of weakly degenerate parabolic equations with memory by means of boundary controls. Unlike the known result for the degenerate parabolic equation, the ... cch reachWebAbstract. We prove null controllability results for the degenerate one-dimensional heat equation ut −(xαux)x = fχω, x ∈(0,1), t∈ (0,T). u t − ( x α u x) x = f χ ω, x ∈ ( 0, 1), t ∈ ( 0, … cch rebuildWebAug 1, 2024 · In this paper, we recover the boundary null controllability for the degenerate heat equation by analyzing the asymptotic behavior of an eligible family of state-control … cch rebuild returnWeban inverse problem for a two-dimensional strongly degenerate heat equation. 2. Statement of the problem and main result In the domain Q T:= f(x;y;t) : 0 bus times in londonWebZhang, Q., Goldstein, J.A. 2001. On a degenerate heat equation with a singular potential. J.Functional Analysis. Vol. 186: 2 p.342-359. ... Some Gradient Estimates for the Heat Equation on Domains and for an Equation by Perelman. International Mathematics Research Notices. p.1-39. (Refereed) ... bus times inverness to dingwall