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Journal articles on the topic 'Measure-valued equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Artstein, Zvi. "On singularly perturbed ordinary differential equations with measure-valued limits." Mathematica Bohemica 127, no. 2 (2002): 139–52. http://dx.doi.org/10.21136/mb.2002.134168.

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2

S. Ackleh, Azmy, Nicolas Saintier, and Jakub Skrzeczkowski. "Sensitivity equations for measure-valued solutions to transport equations." Mathematical Biosciences and Engineering 17, no. 1 (2020): 514–37. http://dx.doi.org/10.3934/mbe.2020028.

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3

Dawson, Donald A., and Zenghu Li. "Stochastic equations, flows and measure-valued processes." Annals of Probability 40, no. 2 (2012): 813–57. http://dx.doi.org/10.1214/10-aop629.

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4

Wang, Feng-Yu. "Itô type measure-valued stochastic differential equations." Journal of Mathematical Analysis and Applications 329, no. 2 (2007): 1102–17. http://dx.doi.org/10.1016/j.jmaa.2006.07.029.

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5

Feshchenko, O. Yu. "On Measure-Valued Processes Generated by Differential Equations." Ukrainian Mathematical Journal 55, no. 4 (2003): 632–42. http://dx.doi.org/10.1023/b:ukma.0000010162.97417.76.

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6

Tesei, Alberto. "Radon measure-valued solutions of quasilinear parabolic equations." Rendiconti Lincei - Matematica e Applicazioni 32, no. 2 (2021): 213–31. http://dx.doi.org/10.4171/rlm/934.

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7

Lanthaler, Samuel, and Siddhartha Mishra. "Computation of measure-valued solutions for the incompressible Euler equations." Mathematical Models and Methods in Applied Sciences 25, no. 11 (2015): 2043–88. http://dx.doi.org/10.1142/s0218202515500529.

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We combine the spectral (viscosity) method and ensemble averaging to propose an algorithm that computes admissible measure-valued solutions of the incompressible Euler equations. The resulting approximate young measures are proved to converge (with increasing numerical resolution) to a measure-valued solution. We present numerical experiments demonstrating the robustness and efficiency of the proposed algorithm, as well as the appropriateness of measure-valued solutions as a solution framework for the Euler equations. Furthermore, we report an extensive computational study of the two-dimension

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8

Rémillard, Bruno, and Jean Vaillancourt. "On signed measure valued solutions of stochastic evolution equations." Stochastic Processes and their Applications 124, no. 1 (2014): 101–22. http://dx.doi.org/10.1016/j.spa.2013.07.003.

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9

Méléard, Sylvie, and Sylvie Roelly. "Discontinuous Measure-Valued Branching Processes and Generalized Stochastic Equations." Mathematische Nachrichten 154, no. 1 (1991): 141–56. http://dx.doi.org/10.1002/mana.19911540112.

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10

Camilli, Fabio, Raul De Maio, and Andrea Tosin. "Measure-valued solutions to nonlocal transport equations on networks." Journal of Differential Equations 264, no. 12 (2018): 7213–41. http://dx.doi.org/10.1016/j.jde.2018.02.015.

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11

Konno, N., and T. Shiga. "Stochastic partial differential equations for some measure-valued diffusions." Probability Theory and Related Fields 79, no. 2 (1988): 201–25. http://dx.doi.org/10.1007/bf00320919.

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12

Illner, Reinhard, and Joachim Wick. "On statistical and measure-valued solutions of differential equations." Journal of Mathematical Analysis and Applications 157, no. 2 (1991): 351–65. http://dx.doi.org/10.1016/0022-247x(91)90094-g.

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13

Nkombo, Quincy Stevene, and Fengquan Li. "Radon Measure-valued Solutions for Nonlinear Strongly Degenerate Parabolic Equations with Measure Data." European Journal of Pure and Applied Mathematics 14, no. 1 (2021): 204–33. http://dx.doi.org/10.29020/nybg.ejpam.v14i1.3877.

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In this paper, we prove the existence of Radon measure-valued solutions for nonlinear degenerate parabolic equations with nonnegative bounded Radon measure data. Moreover, we show the uniqueness of the measure-valued solutions when the Radon measure as a forcing term is diffuse with respect to the parabolic capacity and the Radon measure as a initial value is diffuse with respect to the Newtonian capacity. We also deduce that the concentrated part of the solution with respect to the Newtonian capacity depends on time.

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14

Christoforou, Cleopatra, Myrto Galanopoulou, and Athanasios E. Tzavaras. "Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity." Discrete & Continuous Dynamical Systems - A 39, no. 11 (2019): 6175–206. http://dx.doi.org/10.3934/dcds.2019269.

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15

Porzio, Maria Michaela, and Flavia Smarrazzo. "Radon measure-valued solutions for some quasilinear degenerate elliptic equations." Annali di Matematica Pura ed Applicata (1923 -) 194, no. 2 (2013): 495–532. http://dx.doi.org/10.1007/s10231-013-0386-y.

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16

Orsina, Luigi, Maria Michaela Porzio, and Flavia Smarrazzo. "Measure-valued solutions of nonlinear parabolic equations with logarithmic diffusion." Journal of Evolution Equations 15, no. 3 (2015): 609–45. http://dx.doi.org/10.1007/s00028-015-0275-5.

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17

Porzio, Maria Michaela, Flavia Smarrazzo, and Alberto Tesei. "Radon measure-valued solutions of nonlinear strongly degenerate parabolic equations." Calculus of Variations and Partial Differential Equations 51, no. 1-2 (2013): 401–37. http://dx.doi.org/10.1007/s00526-013-0680-y.

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18

Fjordholm, Ulrik S., Siddhartha Mishra, and Eitan Tadmor. "On the computation of measure-valued solutions." Acta Numerica 25 (May 1, 2016): 567–679. http://dx.doi.org/10.1017/s0962492916000088.

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A standard paradigm for the existence of solutions in fluid dynamics is based on the construction of sequences of approximate solutions or approximate minimizers. This approach faces serious obstacles, most notably in multi-dimensional problems, where the persistence of oscillations at ever finer scales prevents compactness. Indeed, these oscillations are an indication, consistent with recent theoretical results, of the possible lack of existence/uniqueness of solutions within the standard framework of integrable functions. It is in this context that Young measures – parametrized probability m

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19

Demengel, F., and D. Serre. "Nonvanishing singular parts of measure valued solutions for scalar hyperbolic equations." Communications in Partial Differential Equations 16, no. 2-3 (1991): 221–54. http://dx.doi.org/10.1080/03605309108820758.

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20

Ding, Shijin, Boling Guo, and Fengqiu Su. "Measure-valued solution to the strongly degenerate compressible Heisenberg chain equations." Journal of Mathematical Physics 40, no. 3 (1999): 1153–62. http://dx.doi.org/10.1063/1.532826.

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21

Porzio, Maria Michaela, Flavia Smarrazzo, and Alberto Tesei. "Radon Measure-Valued Solutions for a Class of Quasilinear Parabolic Equations." Archive for Rational Mechanics and Analysis 210, no. 3 (2013): 713–72. http://dx.doi.org/10.1007/s00205-013-0666-0.

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22

Alshansky, Maxim. "Differential equations in spaces of Hilbert space valued distributions." Bulletin of the Australian Mathematical Society 68, no. 3 (2003): 491–500. http://dx.doi.org/10.1017/s0004972700037898.

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A Gaussian measure is introduced on the space of Hilbert space valued tempered distributions. It is used to define a Hilbert space valued Q-Wiener process and a white noise process with a nuclear covariance operator Q. The proposed construction is used for solving operator-differential equations with additive noise with the operator coefficient generating an n-times integrated exponentially bounded semigroup.

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23

Gong, Zengtai, Li Chen, and Gang Duan. "Choquet Integral of Fuzzy-Number-Valued Functions: The Differentiability of the Primitive with respect to Fuzzy Measures and Choquet Integral Equations." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/953893.

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This paper deals with the Choquet integral of fuzzy-number-valued functions based on the nonnegative real line. We firstly give the definitions and the characterizations of the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on the nonadditive measure. Furthermore, the operational schemes of above several classes of integrals on a discrete set are investigated which enable us to calculate Choquet integrals in some applications. Secondly, we give a representation of the Choquet integral of a nonnegative, continuous, and increasing fuzzy-number-valued funct

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24

Fornaro, Simona, Stefano Lisini, Giuseppe Savaré, and Giuseppe Toscani. "Measure valued solutions of sub-linear diffusion equations with a drift term." Discrete & Continuous Dynamical Systems - A 32, no. 5 (2012): 1675–707. http://dx.doi.org/10.3934/dcds.2012.32.1675.

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25

Beznea, Lucian, and Andrei-George Oprina. "Bounded and -weak solutions for nonlinear equations of measure-valued branching processes." Nonlinear Analysis: Theory, Methods & Applications 107 (September 2014): 34–46. http://dx.doi.org/10.1016/j.na.2014.04.020.

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26

Del Moral, Pierre, and Arnaud Doucet. "Interacting Markov chain Monte Carlo methods for solving nonlinear measure-valued equations." Annals of Applied Probability 20, no. 2 (2010): 593–639. http://dx.doi.org/10.1214/09-aap628.

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27

Bhatt, Abhay G., G. Kallianpur, and Rajeeva L. Karandikar. "Uniqueness and Robustness of Solution of Measure-Valued Equations of Nonlinear Filtering." Annals of Probability 23, no. 4 (1995): 1895–938. http://dx.doi.org/10.1214/aop/1176987808.

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28

Maniglia, Stefania. "Probabilistic representation and uniqueness results for measure-valued solutions of transport equations." Journal de Mathématiques Pures et Appliquées 87, no. 6 (2007): 601–26. http://dx.doi.org/10.1016/j.matpur.2007.04.001.

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29

Dawson, D. "Stochastic partial differential equations for a class of interacting measure-valued diffusions." Annales de l'Institut Henri Poincare (B) Probability and Statistics 36, no. 2 (2000): 167–80. http://dx.doi.org/10.1016/s0246-0203(00)00121-7.

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30

Kröner, Dietmar, and Wojciech M. Zajaczkowski. "Measure-valued Solutions of the Euler Equations for Ideal Compressible Polytropic Fluids." Mathematical Methods in the Applied Sciences 19, no. 3 (1996): 235–52. http://dx.doi.org/10.1002/(sici)1099-1476(199602)19:3<235::aid-mma772>3.0.co;2-4.

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31

Aleksic, Jelena, and Stevan Pilipovic. "Two scale defect measure and linear equations with oscillating coefficients." Filomat 33, no. 9 (2019): 2867–73. http://dx.doi.org/10.2298/fil1909867a.

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Microlocal measure ? is associated to a two-scale convergent sequence un over Rd with the limit u ? L2(Rd x Td), Td is a torus, to analyze possible strong limit. ? is an operator valued measure absolutely continuous with respect to the product of scalar microlocal defect measure and a measure on the d-dimensional torus. The result is applied to the first order linear PDE with the oscillating coefficients.

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32

SHAMAROV, N. N. "POISSON–MASLOV TYPE FORMULAS FOR SCHRÖDINGER EQUATIONS WITH MATRIX-VALUED POTENTIALS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 10, no. 04 (2007): 641–49. http://dx.doi.org/10.1142/s0219025707002877.

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Cauchy problems for Schrödinger equations with matrix-valued potentials are explicitly solved under following assumptions:. — equations are written in momentum form;. — the potentials are Fourier transformed matrix-valued measures with, in general, noncommuting values;. — initial Cauchy data are good enough. The solutions at time t are presented in form of integrals over some spaces of piecewise continuous mappings of the segment [0, t] to a finite-dimensional momentum space, and measures of the integration are countably additive but matrix-valued (resulting in matrices of ordinary Lebesgue in

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33

KOTELENEZ, PETER M., and BRADLEY T. SEADLER. "ON THE HAHN–JORDAN DECOMPOSITION FOR SIGNED MEASURE VALUED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS." Stochastics and Dynamics 12, no. 01 (2012): 1150009. http://dx.doi.org/10.1142/s0219493712003584.

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Let N-point particles be distributed over ℝd, d ∈ ℕ. The position of the ith particle at time t will be denoted r(t, qi) where qi is the position at t = 0. mi ∈ ℝ\{0} is the "weight" of the ith particle. Let δr be the point measure concentrated in r and [Formula: see text] the initial mass distribution of the N-point particles. The empirical mass distribution (also called the "empirical process") at time t is then given by [Formula: see text] i.e. by the N-particle flow. In Kotelenez (2008) the weights are positive and the motion of the positions of the point particles is described by a stocha

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34

Mazzucchi, S. "Probabilistic Representations for the Solution of Higher Order Differential Equations." International Journal of Partial Differential Equations 2013 (July 17, 2013): 1–7. http://dx.doi.org/10.1155/2013/297857.

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A probabilistic representation for the solution of the partial differential equation (∂/∂t)u(t,x)=−αΔ2u(t,x),α∈ℂ, is constructed in terms of the expectation with respect to the measure associated to a complex-valued stochastic process.

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35

Wang, Zengyun, Jinde Cao, Zhenyuan Guo, and Lihong Huang. "Generalized stability for discontinuous complex-valued Hopfield neural networks via differential inclusions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2220 (2018): 20180507. http://dx.doi.org/10.1098/rspa.2018.0507.

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Some dynamical behaviours of discontinuous complex-valued Hopfield neural networks are discussed in this paper. First, we introduce a method to construct the complex-valued set-valued mapping and define some basic definitions for discontinuous complex-valued differential equations. In addition, Leray–Schauder alternative theorem is used to analyse the equilibrium existence of the networks. Lastly, we present the dynamical behaviours, including global stability and convergence in measure for discontinuous complex-valued neural networks (CVNNs) via differential inclusions. The main contribution

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36

Ahmed, N. U. "Measure valued solutions for stochastic evolution equations on Hilbert space and their feedback control." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 25, no. 1 (2005): 129. http://dx.doi.org/10.7151/dmdico.1061.

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37

Neustupa, Jiří. "Measure-valued Solutions of the Euler and Navier-Stokes Equations for Compressible Barotropic Fluids." Mathematische Nachrichten 163, no. 1 (1993): 217–27. http://dx.doi.org/10.1002/mana.19931630119.

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38

Casas, Eduardo, and Karl Kunisch. "Optimal Control of the Two-Dimensional Stationary Navier--Stokes Equations with Measure Valued Controls." SIAM Journal on Control and Optimization 57, no. 2 (2019): 1328–54. http://dx.doi.org/10.1137/18m1185582.

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39

Bertsch, Michiel, Lorenzo Giacomelli, and Alberto Tesei. "Measure-Valued Solutions to a Nonlinear Fourth-Order Regularization of Forward-Backward Parabolic Equations." SIAM Journal on Mathematical Analysis 51, no. 1 (2019): 374–402. http://dx.doi.org/10.1137/18m1203821.

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40

Chae, Dongho, and Pavel Dubovskii. "Functional and measure-valued solutions of the euler equations for flows of incompressible fluids." Archive for Rational Mechanics and Analysis 129, no. 4 (1995): 385–96. http://dx.doi.org/10.1007/bf00379261.

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41

Gotoda, Takeshi. "Convergence of filtered weak solutions to the 2D Euler equations with measure-valued vorticity." Journal of Evolution Equations 20, no. 4 (2020): 1485–509. http://dx.doi.org/10.1007/s00028-020-00563-4.

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42

Feireisl, Eduard, Mária Lukáčová-Medvid’ová, and Hana Mizerová. "Convergence of Finite Volume Schemes for the Euler Equations via Dissipative Measure-Valued Solutions." Foundations of Computational Mathematics 20, no. 4 (2019): 923–66. http://dx.doi.org/10.1007/s10208-019-09433-z.

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43

Kim, Jong Uhn. "Measure valued solutions to the stochastic Euler equations in $$\mathbb {R}^d$$ R d." Stochastic Partial Differential Equations: Analysis and Computations 3, no. 4 (2015): 531–69. http://dx.doi.org/10.1007/s40072-015-0060-z.

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44

Casas, Eduardo, and Karl Kunisch. "Optimal Control of the Two-Dimensional Evolutionary Navier--Stokes Equations with Measure Valued Controls." SIAM Journal on Control and Optimization 59, no. 3 (2021): 2223–46. http://dx.doi.org/10.1137/20m1351400.

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45

Smarrazzo, Flavia. "On a Class of Quasilinear Elliptic Equations with Degenerate Coerciveness and Measure Data." Advanced Nonlinear Studies 18, no. 2 (2018): 361–92. http://dx.doi.org/10.1515/ans-2017-6032.

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AbstractWe study the existence of measure-valued solutions for a class of degenerate elliptic equations with measure data. The notion of solution is natural, since it is obtained by a regularization procedure which also relies on a standard approximation of the datum μ. We provide partial uniqueness results and qualitative properties of the constructed solutions concerning, in particular, the structure of their diffuse part with respect to the harmonic-capacity.

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46

Wang, Jingyu, Yejuan Wang, and Dun Zhao. "Pullback attractors for multi-valued non-compact random dynamical systems generated by semi-linear degenerate parabolic equations with unbounded delays." Stochastics and Dynamics 16, no. 05 (2016): 1750001. http://dx.doi.org/10.1142/s0219493717500010.

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The theory of pullback attractors for multi-valued non-compact random dynamical systems and a method of asymptotic compactness based on the concepts of the Kuratowski measure of the non-compactness of a bounded set are used to prove the existence of pullback attractors for the multi-valued non-compact random dynamical systems associated with the semi-linear degenerate parabolic unbounded delay equations with both deterministic and random external terms.

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47

Qiao, Huijie. "Uniqueness for measure-valued equations of nonlinear filtering for stochastic dynamical systems with Lévy noise." Advances in Applied Probability 50, no. 2 (2018): 396–413. http://dx.doi.org/10.1017/apr.2018.19.

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Abstract In the paper we study the Zakai and Kushner–Stratonovich equations of the nonlinear filtering problem for a non-Gaussian signal-observation system. Moreover, we prove that under some general assumption, the Zakai equation has pathwise uniqueness and uniqueness in joint law, and the Kushner–Stratonovich equation is unique in joint law.

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48

Baker, John A. "Functional Equations, Distributions and Approximate Identities." Canadian Journal of Mathematics 42, no. 4 (1990): 696–708. http://dx.doi.org/10.4153/cjm-1990-036-1.

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The subject of this paper is the use of the theory of Schwartz distributions and approximate identities in studying the functional equationThe aj’s and b are complex-valued functions defined on a neighbourhood, U, of 0 in Rm, hj. U → Rn with hj(0) = 0 and fj, g: Rn → C for 1 ≦ j ≦ N. In most of what follows the aj's and hj's are assumed smooth and may be thought of as given. The fj‘s, b and g may be thought of as the unknowns. Typically we are concerned with locally integrable functions f1, … , fN such that, for each s in U, (1) holds for a.e. (almost every) x ∈ Rn, in the sense of Lebesgue me

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49

Bonanno, Gabriele, та Salvatore A. Marano. "Elliptic problems in ℝN with discontinuous nonlinearities". Proceedings of the Edinburgh Mathematical Society 43, № 3 (2000): 545–58. http://dx.doi.org/10.1017/s0013091500021180.

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AbstractFor a class of elliptic equations in the entire space and with nonlinear terms having a possibly uncountable (but of Lebesgue measure zero) set of discontinuities, the existence of strong solutions is established. Two simple applications are then developed. The approach taken is strictly based on set-valued analysis and fixed-points arguments.

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50

GWIAZDA, PIOTR, and ANNA MARCINIAK-CZOCHRA. "STRUCTURED POPULATION EQUATIONS IN METRIC SPACES." Journal of Hyperbolic Differential Equations 07, no. 04 (2010): 733–73. http://dx.doi.org/10.1142/s021989161000227x.

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In this paper, a framework for the analysis of measure-valued solutions of the nonlinear structured population model is presented. Existence and Lipschitz dependence of the solutions on the model parameters and initial data are shown by proving convergence of a variational approximation scheme, defined in the terms of a suitable metric space. The estimates for a corresponding linear model are used based on the duality formula for transport equations. An extension of a Wasserstein metric to the measures with integrable first moment is proposed to cope with the nonconservative character of the m

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