où les coefficients sont des fonctions mesurables appartenant à espaces L * (Ω) convenables dans un ouvert borné Ω de R n . Le but principal est d’étendre résultat [par W. Littman, G. Stampacchia et H. Weinberger] sur points réguliers pour le problème Dirichlet équations plus générales (§10). paragraphe 3 contient aussi principe maximum solutions faibles. 4 majorations a priori p solutions.

For a 2 × reaction–diffusion system on bounded domain, we give simultaneous stability result for one coefficient and the initial conditions. The key ingredient is global Carleman-type estimate with single observation acting subdomain.

We consider a 2 × system of parabolic equations with first and zeroth coupling establish Carleman estimate by extra data only one component without initial values. Then we apply the to inverse problems determining some or all coefficients observations in an arbitrary subdomain over time interval two components at fixed positive θ whole spatial domain. The main results are Lipschitz stability estimates for problems. For stability, have assume non-degeneracy condition it, can approximately...

We study parameter estimation for one-dimensional energy balance models with memory (EBMMs) given localized and noisy temperature measurements. Our results apply to a wide range of nonlinear, parabolic partial differential equations integral terms. First, we show that space-dependent can be determined uniquely everywhere in the PDE's domain definition <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:mi...

We present a controllability result for class of linear parabolic systems $3$ equations. establish global Carleman estimate the solutionsof $2$ equations coupled with first order terms. Stability results inverse coefficients problems are deduced.

We consider the inverse problem of determining isotropic inhomogeneous electromagnetic coefficients non-stationary Maxwell equations in a bounded domain , from finite number boundary measurements. Our main result is Hölder stability estimate for problem, where measurements are exerted only some components. For it, we prove global Carleman heterogeneous system under conditions.

We consider the multidimensional inverse problem of determining conductivity coefficient a hyperbolic equation in an infinite cylindrical domain, from single boundary observation solution. prove Hölder stability with aid Carleman estimate specifically designed for waveguides.

We consider the inverse problem of determining time-dependent magnetic field Schrödinger equation in a bounded open subset , from finite number Neumann data, when boundary measurement is taken on an appropriate boundary. prove Lipschitz stability potential Coulomb gauge class by n times changing initial value suitably.

We consider the operator H := i∂ t + ∇ . ( c ∇) in an unbounded strip Ω ℝ 2 , where prove adapted global Carleman estimate and energy for this operator. Using these estimates, we give a stability result diffusion coefficient x y ).

This paper is devoted to the analysis of some uniqueness properties a classical reaction-diffusion equation Fisher-KPP type, coming from population dynamics in heterogeneous environments. We work one-dimensional interval $(a,b)$ and we assume nonlinear term form $u \, (\mu(x)-\gamma u)$ where $\mu$ belongs fixed subset $C^{0}([a,b])$. prove that knowledge $u$ at $t=0$ $u$, $u_x$ single point $x_0$ for small times $t\in (0,\varepsilon)$ sufficient completely determine couple $(u(t,x),\mu(x))$...

In this paper, we prove a uniqueness result in the inverse problem of determining several non-constant coefficients one-dimensional reaction-diffusion equations. Such equations include classical model Kolmogorov, Petrovsky and Piskunov as well more sophisticated models from biology. When reaction term contains an unknown polynomial part degree $N,$ with $\mu_k(x),$ our gives sufficient condition for determination part. This only involves pointwise measurements solution $u$ equation its...

We consider the inverse problem of determining two non-constant coefficients in a nonlinear parabolic equation Fisher–Kolmogorov–Petrovsky–Piskunov type. For ut = DΔu + μ(x) u − γ(x)u2 (0, T) × Ω, which corresponds to classical model population dynamics bounded heterogeneous environment, our results give stability inequality between couple (μ, γ) and some observations solution u. These consist measurements u: whole domain Ω at fixed times, subset ω⊂⊂Ω during finite time interval on boundary...

We consider the inverse problem of simultaneous reconstruction dielectricpermittivity and magnetic permeability functions Maxwell's system in3D with limited boundary observations electric field. Thetheoretical stability for is provided by Carleman estimates.For numerical computations formulated as anoptimization hybrid finite element/difference method isused to solve parameter identification problem.

We consider an inverse problem of reconstructing two spatially varying coefficients in acoustic equation hyperbolic type using interior data solutions with suitable choices initial condition. Using a Carleman estimate, we prove Lipschitz stability estimates which ensures unique reconstruction both coefficients. Our theoretical results are justified by numerical studies on the unknown noisy backscattered data.

In this paper, we prove a uniqueness result in the inverse problem of determining several non-constant coefficients system two parabolic equations, which corresponds to Lotka–Volterra competition model. Our gives sufficient condition for determination four system. This only involves pointwise measurements solution (u, v) and spatial derivative ∂u/∂x or ∂v/∂x one component at single point x0, during time interval (0, ε). results are illustrated by numerical computations.

Abstract In this article, we consider a nonlinear parabolic system with two components and prove stability estimate of Lipschitz type in determining coefficients the by data only one component. The main idea for proof is Carleman estimate. Keywords: systemsinverse problemCarleman estimateLipschitz estimateAMS Subject Classifications: 35K4035K5535K57 Acknowledgement This work was supported JSPS-CNRS Bilateral Joint Project.

We study the inverse problem of simultaneous identification two discontinuous diffusion coefficients for a one-dimensional coupled parabolic system with observation only one component. The stability result is obtained by Carleman-type estimate. Results from numerical experiments in case are reported, suggesting that method makes possible to recover coefficients.

This paper is concerned with the determination of coefficients and source term in a strong coupled quantitative thermoacoustic system equations. Adapting Carleman estimate established part I this series papers, we prove stability estimates Hölder type involving observation only one component: temperature or pressure.

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