Degenerate heat equation

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August undefined, 2024

Weban 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 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 …

On a general degenerate/singular parabolic equation with a …

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. WebAn inverse problem for strongly degenerate heat equation M. Ivanchov, N. Saldina Mathematics 2006 In this paper we consider an inverse problem for determining time-dependent heat conduction coefficient which vanishes at initial moment as a power tβ . The case of strong degeneration (β ≥ 1) is… 21 PDF View 1 excerpt, references background university of st andrews template

Wright–Fisher Diffusion in One Dimension SIAM Journal on …

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) … 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. WebDec 31, 2004 · Abstract: We prove null controllability results for the degenerate one-dimensional heat equation $$ u_t - (x^\alpha u_x)_x = f \chi _\omega , \quad x\in (0,1), \ \ t\in (0,T) .$$ 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. university of st andrews visa

Entropy Free Full-Text Quantum Thermodynamics with Degenerate …

Unicity of solution for a semi-infinite inverse heat source problem

WebSep 1, 2008 · In this paper we consider the approximate controllability of a class of degenerate systems. The equations may be weakly degenerate and strongly degenerate on the boundary. We prove that the... 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 ... rebound velocity formulaWebWe will classify these equations into three diﬀerent categories. Ifb2¡4ac >0, we say the equation is hyperbolic. Ifb2¡4ac= 0, we say the equation is parabolic. If b2¡4ac <0, we say the equation is elliptic. Example 1. †The wave equation utt¡uxx= 0 is hyperbolic: †The Laplace equation uxx+uyy= 0 is elliptic: †The heat equation university of st andrews web print

"WebSep 9, 2024 · This paper investigates the nonnegative approximate controllability for the one-dimensional degenerate heat equation governed by bilinear control. Both non … " - Degenerate heat equation

Degenerate heat equation

Determination of Time-Dependent Coefficients for a Weakly …

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 … WebAug 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 …

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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 … 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.

WebThese are lecture notes on parabolic di erential equations, with a focus on estimates in H older spaces. The two main goals of our dis-cussion are to obtain the parabolic Schauder estimate and the Krylov- ... 2.3 Schauder estimates for the heat equation . . . . . . . .18 2.4 Interior Schauder estimates for linear parabolic equations20 Webdegenerate gas, in physics, a particular configuration, usually reached at high densities, of a gas composed of subatomic particles with half-integral intrinsic angular momentum …

WebWe are mainly interested in the situation of a degenerate equation at the boundary i.e. in the case where a (0)=0 and / or a (1)=0. A typical example is a ( x )= xα (1 − x) β with α, β ∈ [0, 2). As a consequence, we deduce null controllability results for the degenerate one … WebFeb 1, 2005 · In this section, we prove the null controllability for the following nonhomogeneous, degenerate, singular heat equations using a new modified …

WebMar 15, 2024 · It should be noted that when α ≥ 1, the heat equation becomes the so-called “strongly” degenerate one, the uniform Neumann condition for “heat” part always holds at the degenerate point (or line) x = 0 (see Cannarsa et al. [9], [10]), and the well-posedness and decay rate for this case are still open.

WebIn 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 ... university of st andrews risk assessmentWebA 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 … university of stanford software licensingWebAug 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 … rebound vancouver wa hoursWebJul 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... rebound velocity calculatorWebFeb 29, 2016 · Jérôme Le Rousseau, Carleman estimates and controllability results for the one-dimensional heat equation with BV coefficients, J. Differential Equations 233 (2007), no. 2, ... Carleman estimates for one-dimensional degenerate heat equations, J. Evol. Equ. 6 (2006), no. 2, 325–362. rebound vasodilationWebAbstract. 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 rebound vancouver clinicWebThe 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. rebound vancouver washington