# A Uniqueness Theorem For A Class Of Nonlinear Parabolic Inverse Problems

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### NONNEGATIVE CONTROLLABILITY FOR A CLASS OF

by G FLORIDIA 2020 Cited by 2 NONLINEAR DEGENERATE PARABOLIC EQUATIONS WITH In Theorem 1.4 below, we obtain an optimal goal, that is, we approximately The proofs of the existence and uniqueness results for strict and strong solutions An important class of biomedical reaction-diffusion problems consists in the.

### 1150.pdf - University of Minnesota

by G Bao 1993 Cited by 75 A UNIQUENESS THEOREM FOR AN INVERSE PROBLEM the study of a class of optimal design problems where one wishes to design a periodic Suzanne M. Lenhart & Jiongmin Yong, Optimal control for degenerate parabolic equations with Gang Bao & David C. Dobson, Second harmonic generation in nonlinear

### Kabanikhin, SI; Lorenzi, A. 击Identification problems of - ORBi

by P Rochus 1999 This book introduces and analyzes a wide class of inverse problems related to wave propagation, and engineers: the main theoretical results (existence, uniqueness, conditional stability) are As a rule, inverse problems are essentially nonlinear and when studying inverse problems for elliptic or parabolic equations.

### A TRACE-TYPE FUNCTIONAL METHOD FOR

by JIN WEN 2017 The inverse problem of identifying coefficient q(x) in the following parabolic equation the authors in [16] considered the uniqueness theorem by the uniqueness of the solution of On a class of nonlinear parabolic equations with nonlinear.

### Approximation Methods for Inverse Problems Governed by

by HT Banksy 1999 Cited by 10 Keywords: Inverse problems, nonlinear parabolic systems, We multiply the ith equation in (1) by a function i in a suitable class of test Theorem 2 Under conditions A1){A6) the system (6) has a unique weak solution y 2.

### Determination of an unknown function in a parabolic equation

In this paper we consider the parabolic inverse problem of finding one of the in the class of positive functions and left the existence as an open question. An An existence theorem as well as uniqueness for the solution of this J. R. and Yin, H. M., 'A class of nonlinear nonclassical parabolic problems', J. Dt$ Eqs, 79,. 12.

### Galerkin time-stepping methods for nonlinear parabolic

by G Akrivis 2004 Cited by 67 Continuous Galerkin methods for the above class of nonlinear parabolic equations. local uniqueness of the discontinuous Galerkin approximations for problem (1.1). In the sequel, we will also use the following well-known inverse inequalities the discontinuous Galerkin method is given in the following theorem:

### Multidimensional Inverse and Ill-Posed Problems for

by VG Romanov Cited by 61 2.5 An Uniqueness Theorem for the Solution of an Inverse Problem multidimensional inverse problem for the Schrцdinger equation in the class of tions for certain nonlinear inverse problems for differential equations, using a parabolic.

### Existence and Uniqueness Results for an Inverse Problem for

by AU Sazaklioglu 2017 Cited by 12 Keywords. semilinear parabolic equations,inverse problem, finite difference method, dimensional open dynamical systems to solve a nonlinear source identification problem. Moreover, theorems on unique solvability of this [15] I. Orazov, M. A. Sadybekov, On a class of problems of determining the temperature and

### N00014-89-J-1008 - DTIC

by MS Pilant 1989 Cited by 14 have developed for use in elliptic and parabolic inverse problems. Both types of inverse problem leads to nonlinear equations, and H. M. Yin, A uniqueness theorem for a class of parabolic inverse problems, J. Inverse.

### On solvability of inverse problem for one equation of - Tübitak

by ART QIZI 2020 The existence and uniqueness of the integral equation are proved by class of nonlocal problems for partial differential equations. one of the coefficients are unknown, then the inverse problem will be nonlinear. Theorem 2.3 Let φ(x),ψ(x) ∈ C[0, 1],h(t) ∈ C2[0,T],h(t) ̸= 0, (0 ≤ t ≤ T), f(x, t) ∈ C(DT ),.

### Finite time blow up of solutions to an inverse problem - EMIS

by S Gür Cited by 3 Existence and uniqueness of solutions to inverse problems for parabolic equations are studied less is known about inverse problem for nonlinear parabolic equations. Theorem 2.1. problem for a class of nonlinear parabolic equations.

### PARABOLİK DENKLEMLERDE BİLİNMEYEN - CiteSeerX

by BMA DALI 2002 Parabolic equation, inverse problem, source parameter, unknown coefficient, initial- Nonlinear Diffusion Equation Subject to the Specification of Mass, SIAM J. [10] Cannon, J.R., Yin, H.M. (1988c) A Uniqueness Theorem for a Class of.

### (C2) J /3(u) - J-Stage

by N KENMOCHI 1982 Cited by 3 This kind of problems for a certain class of nonlinear parabolic equations was treated earlier In order to demonstrate the above existence theorem we introduce a map- ping P from a certain Also let p be the inverse o f j3. Then. I(t; v, ~1)=

### A uniqueness theorem for a class of nonlinear parabolic

by JR Cannon 1988 Cited by 24 In this paper, we give a uniqueness theorem for a class of nonlinear parabolic inverse problems by means of integral estimates which appeared in Baiocchi et

### EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR

by P Chen 2017 Cited by 3 CLASS OF NONLINEAR PARABOLIC EQUATIONS. PEIYING CHEN Existence, uniqueness, weak solution, variation problem, N-function. the right-inverse function of φ. Clearly, ψ also Lemma 2.10 (De La Vallée Poussin's Theorem [2]).

### ON A NONLOCAL INVERSE PROBLEM WITH THE

by EI Azizbayov 2017 Cited by 1 The existence and uniqueness theorem for a classical solution is proved Key Words: inverse value problem, parabolic equation of second is the class of non-local problems for differential equations in partial deriva a Class of Pseudohyperbolic Equations of Third Order with Non-Linear Operator Right.

### Inverse problems for linear and non-linear hyperbolic - IMPA

inverse problems non-linear hyperbolic equations and systems, and consider the [1992] and Tataru's unique continuation theorem Tataru [1995] gave a topology, differentiable structure and the conformal class of the metric g in the double On uniqueness in inverse problems for semilinear parabolic equations

### Nonlinear boundary value problems for a parabolic equation

by N Gol dman solvability in a class of smooth functions are obtained on the basis of the Rothe method. Unique solvability of a nonlinear parabolic problem with the In order to prove Theorem 3.1 and to establish the existence of the N. L. Gol'dman, Inverse Stefan Problems, Dordrecht: Kluwer Academic, 1997. 4.

### Working Paper Control Reconstruction for Nonlinear Parabolic

by VI Maksimov 1994 Cited by 6 The problem of reconstruction of a control for nonlinear parabolic equations is con- of inverse problems of dynamics that are being inversely studied today (see, (Theorem of Benilan, see Lakshmikantham and Leela, [20, Theorem 3.5.1, p. In this (special) case we assume xo E H. Then there exists a unique strong

### A class of inverse problems for nonlinear parabolic equations

by MV Klibanov 1986 Cited by 50 In the present paper we obtain uniqueness theorems for a one-dimensional inverse prob- lem of determining n coefficients of a nonlinear parabolic equation

### Introduction

This nonlinear problem is reduced to an operator equation whose solvability is and uniqueness theorem for solutions to the problem (1) (3). Pyatkov S.G., Samkov M.L. On Some Classes of Coe cient Inverse Problems for Parabolic.

### PERIODIC SOLUTIONS OF CERTAIN NONLINEAR

by Y Yamada 1978 Cited by 29 In this paper we consider the periodic problems for certain nonlinear parabolic differential equations in domains with periodically moving uniqueness theorem (Theorem 1.4) for the abstract nonlinear differential Γa(f) (a = 1,2, ,ί) which are sufficiently smooth (say, of class C2) and satisfy where both X and its inverse X'1.

### Determination of a time-dependent parameter in a one

class of physical phenomena is modelled by non-classical parabolic The existence and uniqueness of the solution of these inverse problems are established and numerical approximations of both linear and nonlinear problems [21]. In next theorem, the stability of the Adomian decomposition method is shown, i.e. it is.

### Nonlinear Analysis Perturbation method for abstract second

by F Awawdeh 2010 Cited by 9 As a possible application of the abstract theorems, For the inverse problem (1a) (1c) we raise the questions of existence and uniqueness of a [9] M. Klibanov, One class of inverse problems for nonlinear parabolic equations, Doklady

### Solutions to Nonlinear Evolutionary Parabolic - MDPI

by A Kazakov 2021 Keywords: nonlinear parabolic equation; porous medium equation; for a class of nonclassical diffusion equations in a smooth bounded the problem of a diffusion wave motion with a specified front for Equation (1). Let us formulate and prove the existence theorem of locally analytical solutions to.

### ON THE UNIQUENESS OF NONLINEAR DIFFUSION

by H Egger 2017 Cited by 2 Uniqueness for this inverse in an appropriate class G of Dirichlet data and for coefficient functions a, b, c, The identification of parameters in nonlinear parabolic problems from one of the central arguments for the proof of Theorem 1.

### Some new statements for nonlinear parabolic problems

by NL Gol'dman 2021 to a class of ill-posed boundary inverse problems but it has an essential distinction from 2 Unique solvability of a nonlinear parabolic problem with an unknown solution {u(x, t),ρ(x, t)} of system (1) (4) is given in the following theorem.

### Proceedings of the NATIONAL ACADEMY OF - PNAS

uniqueness theorems for solutions of nonlinear boundary value problems for various classes of nonlinear partial differential equations. Very recently Then T is a one-to-one mapping of X onto X* with a continuous inverse: We note 8 Browder, F. E., Strongly nonlinear parabolic boundary value problems, Amer. J. Math.,.

### A Class of Non-linear Non-classical Parabolic Equations

by JR Cannon 1989 Cited by 140 consider the following inverse problem of finding u(x, t) and p(t) J. R. CANNON AND H. M. YIN, A uniqueness theorem for a class of nonlinear parabolic.

### A NONLINEAR PARABOLIC INVERSE - Imm.Az

by AY AKHUNDOV Cited by 2 In the paper a nonlinear second order parabolic inverse coefficent problem In papers [2, 3, 5] the uniqueness theorems of one-dimesional inverse problems Problem (1)-(3) relates to the class of incorrect by Hadamard problems therefore.

### REFERENCE - International Atomic Energy Agency

theorem to conclude that an appropriate unique solution to this problem exists. Inverse problems for nonlinear diffusion problems have been studied by many class of admissible coefficients, there will exist a unique solution c(x,t) of the direct where C(x,t;^,i) is the fundamental solution of parabolic equations defined by

### ICASE REPORT NO. 88-26 - NASA Technical Reports Server

by HT Banks 1988 Cited by 44 Inverse problems for nonlinear systems governed by strongly maximal mone define a class of nonlinear distributed systems and the associated parameter nonlinear parabolic partial differential equations to which they lead. In particular linear semigroups, to prove the theorem via an application of our existence result

### Acta Mathematica Sinica, English Series

by YH OU 2008 Cited by 30 Keywords Parabolic equations, Inverse coefficient problems, Existence of quasisolutions. MR(2000) Subject nonlinear parabolic initial boundary value problems. ⎧ However wide class of inverse problems of computa- and then obtain the main result, the existence theorem for the inverse problem.

### The nonlocal inverse problem of the identification of the lowest

by EI Azizbayov 2019 Cited by 5 for the existence and uniqueness of the classical solution to inverse problem of a Keywords: Inverse problem; Parabolic equation; Overdetermination Theorem 1.2 ([27]) Suppose that the following conditions are satisfied: δ ≥ 0, 0 < c(t) ∈ A.: On a class of forward backward parabolic equations: existence of solutions.

### EXISTENCE-UNIQUENESS AND LONG TIME BEHAVIOR

by A Ackleh 2000 Cited by 35 to a class of nonlinear reaction-diffusion problems that arise in Nonlocal parabolic evolution equations, unbounded diffusion, popu- then (3.2) has a global classical solution v (see Theorem 7.1, page 83 in [12]). [4] H. T. Banks, S. Reich and I. G. Rosen, Galerkin Approximation for Inverse Problems for.

### Renormalized solutions of nonlinear parabolic equations with

by F Petitta Cited by 94 9 A partial uniqueness result and inverse maximum principle In [11] the authors extend the result of existence and uniqueness to a larger class of measures which Renormalized solutions, parabolic problems with measures. 3 Theorem 1 Let µ be a bounded measure on Q. If µ ∈ M0(Q) then there exist h ∈ Lp (0,T;

### IDENTIFICATION OF THE DENSITY DEPENDENT

by R TINAZTEPE 2014 Cited by 5 The density dependent nonlinear reaction-diffusion equation ut = (a(u)ux)x method to solve the inverse problem for a special class of admissible coefficients. But the existence and uniqueness theorem also holds for the inverse problem [8] Friedman, A. Partial Differential Equations of Parabolic Type.

### The inverse problem of determining several coefficients in a

by L Roques 2012 Cited by 24 In this paper, we prove a uniqueness result in the inverse problem of of two nonlinear parabolic equations, using only local or boundary measurements. In the next section, Theorem 2.1 shows that these measurements are sufficient to Uniqueness in the large of a class of multidimensional inverse.

### Existence results for inverse problems associated with - CORE

by A Zeghal 2002 Cited by 22 associated with a nonlinear parabolic equation The inverse problem is first reduced to a nonlinear operator equation and then (1) It is well known (see, for instance, [10, Theorem 4.2.1] or a class of overposed data q satisfying (H4).

### Stable estimation of two coefficients in a nonlinear - Hal Inrae

by M Cristofol 2013 Cited by 14 Keywords: Inverse Problem Nonlinear parabolic equation Two coefficients Stability Such stability inequalities lead to the uniqueness of the coefficients Before stating our main theorem, let us state a preliminary lemma which gives a Uniqueness in the large of a class of multidimensional inverse.

### Carleman estimates for global uniqueness, stability and

by MV Klibanov 2012 Cited by 153 2.3 Derivation of the Carleman estimate for a parabolic operator Uniqueness theorems for multidimensional inverse problems broad class of inverse problems for those equations Pu = f for which the solution of the Cauchy problem of the QRM and the conventional one is that MCIPs are nonlinear.

### Determination of the insolation function in the nonlinear

by J Tort 2012 Cited by 24 of some 1-dimensional nonlinear parabolic problem with degenerate diffusion. references dealing with uniqueness results for parabolic inverse problems, for of some inverse source problem for a class of linear degenerate parabolic equations. particular in [7], Lemma 2.5 and Theorems 2.3 and 2.8.

### Publications 1. An abstract Cauchy Kovalevska theorem in

An abstract Cauchy Kovalevska theorem in Gevrey classes, Symposia Math (VII) New proofs and generalizations of theorems of existence and uniqueness for An inverse problem for a nonlinear diffusion equation, SIAM JAP, 1980 (with J R Inverse problems for parabolic partial differential equations, ISNM 77, Inverse.

### SOME INVERSE PROBLEMS FOR CONVECTION

by SG Pyatkov Cited by 7 We prove an existence and uniqueness theorem, as well as stability estimates. reader can nd statements of inverse problems for parabolic equations and systems and Assume that G is a bounded domain with boundary of class C2, the conditions An Inverse Coe cient Problem with Nonlinear Parabolic Equation / Jing.

### SOLVABILITY OF A CLASS OF PARABOLIC INVERSE

by HM Yin 1996 Cited by 15 In this paper we study a class of parabolic inverse problems where unknown We shall use Schauder's fixed-point theorem to prove the local existence. argument to show the local existence as long as the fully nonlinear parabolic problem.

### Research Article Conditional Well-Posedness for an Inverse

by C Sun Cited by 1 on inverse problems for parabolic equations since 1970s. As for general [6] J. R. Cannon and H. Yin, A uniqueness theorem for a class of nonlinear with a nonlinear parabolic equation, Journal of Mathematical. Analysis

### Improperly Posed Problems in Partial Differential - SIAM

by LE Payne 1975 Cited by 471 M. BERZANS[at, A uniqueness theorem in the inverse spectral problem lor The backward beam equation: Two A-stable schemes for parabolic problems, SIAM [99] T. DUSHANE, On existence and uniqueness for a new class of non-linear

### Multidimensional Inverse Boundary Value Problem for a

by MA Guliev (1988), the example of a parabolic equation given way to explore the problem of solvability for some nonlinear inverse problems for differential equations. for solutions of multidimensional inverse boundary value problems in classes of functions equations and then proved the existence and uniqueness theorems for the

### PDF PDF - De Gruyter

ary point for the one-dimensional inverse problem in two-dimensional space. Journal of Inverse and Existence results for parabolic identification problems. On a class of nonlinear convo- The unique solvability theorem for a one-dimen-.