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Relevant bibliographies by topics / Fully nonlinear PDE

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Journal articles

Academic literature on the topic 'Fully nonlinear PDE'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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Journal articles on the topic "Fully nonlinear PDE"

1

Sirakov, Boyan. "Solvability of Uniformly Elliptic Fully Nonlinear PDE." Archive for Rational Mechanics and Analysis 195, no. 2 (2009): 579–607. http://dx.doi.org/10.1007/s00205-009-0218-9.

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2

Lions, Pierre-Louis, and Panagiotis E. Souganidis. "Fully nonlinear stochastic pde with semilinear stochastic dependence." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 331, no. 8 (2000): 617–24. http://dx.doi.org/10.1016/s0764-4442(00)00583-8.

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3

Wei-an, Liu, and Lu Gang. "Viscosity solutions of fully nonlinear functional parabolic PDE." International Journal of Mathematics and Mathematical Sciences 2005, no. 22 (2005): 3539–50. http://dx.doi.org/10.1155/ijmms.2005.3539.

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By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown. Then the existence and uniqueness are established by the fixed point theory.

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4

Wang, Falei. "Comparison Theorem for Nonlinear Path-Dependent Partial Differential Equations." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/968093.

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We introduce a type of fully nonlinear path-dependent (parabolic) partial differential equation (PDE) in which the pathωton an interval [0,t] becomes the basic variable in the place of classical variablest,x∈[0,T]×ℝd. Then we study the comparison theorem of fully nonlinear PPDE and give some of its applications.

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5

Ikoma, Norihisa, and Hitoshi Ishii. "Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 29, no. 5 (2012): 783–812. http://dx.doi.org/10.1016/j.anihpc.2012.04.004.

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6

Katzourakis, Nikos. "Generalised solutions for fully nonlinear PDE systems and existence–uniqueness theorems." Journal of Differential Equations 263, no. 1 (2017): 641–86. http://dx.doi.org/10.1016/j.jde.2017.02.048.

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7

Wang, Zhi Yu. "Finite Strain Analysis of Crack Tip Fields in Yeoh-Model-Based Rubber-Like Materials which Are Loaded in Plane Stress." Applied Mechanics and Materials 127 (October 2011): 477–83. http://dx.doi.org/10.4028/www.scientific.net/amm.127.477.

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The dominant asymptotic stress feild near the tip of a Mode-I crack of Yeoh-model-based rubber-like materials is determined. The analysis bases on the fully nonlinear equilibrium theory of incompressible hyperelastic solids. First, The nonlinear PDE (partial differential equation) governig the leading behavior of y2 is transformed to a linear PDE. Then the linear PDE is solved and the solution of y2 is obtained. With the solution of y2 and boundery conditions the numerical solution of y1 is obtained,too.Finally,the analysis solution in polar coordinate of the first Kirchhoff Stress in plane st

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8

Zhang, Jianfeng, and Jia Zhuo. "Monotone schemes for fully nonlinear parabolic path dependent PDEs." Journal of Financial Engineering 01, no. 01 (2014): 1450005. http://dx.doi.org/10.1142/s2345768614500056.

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In this paper, we extend the results of the seminal work Barles and Souganidis (1991) to path dependent case. Based on the viscosity theory of path dependent PDEs, developed by Ekren et al. (2012a, 2012b, 2014a and 2014b), we show that a monotone scheme converges to the unique viscosity solution of the (fully nonlinear) parabolic path dependent PDE. An example of such monotone scheme is proposed. Moreover, in the case that the solution is smooth enough, we obtain the rate of convergence of our scheme.

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9

Panayotounakos, D. E., and K. P. Zafeiropoulos. "General solutions of the nonlinear PDEs governing the erosion kinetics." Mathematical Problems in Engineering 8, no. 1 (2002): 69–85. http://dx.doi.org/10.1080/10241230211379.

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We present the construction of the general solutions concerning the one-dimensional (1D) fully dynamic nonlinear partial differential equations (PDEs), for the erosion kinetics. After an uncoupling procedure of the above mentioned equations a second–order nonlinear PDE of the Monge type governing the porosity is derived, the general solution of which is constructed in the sense that a full complement of arbitrary functions (as many as the order) is introduced. Afterwards, we specify the above solution according to convenient initial conditions.

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10

Ayanbayev, Birzhan, and Nikos Katzourakis. "On the Inverse Source Identification Problem in $L^{\infty }$ for Fully Nonlinear Elliptic PDE." Vietnam Journal of Mathematics 49, no. 3 (2021): 815–29. http://dx.doi.org/10.1007/s10013-021-00515-6.

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AbstractIn this paper we generalise the results proved in N. Katzourakis (SIAM J. Math. Anal. 51, 1349–1370, 2019) by studying the ill-posed problem of identifying the source of a fully nonlinear elliptic equation. We assume Dirichlet data and some partial noisy information for the solution on a compact set through a fully nonlinear observation operator. We deal with the highly nonlinear nonconvex nature of the problem and the lack of weak continuity by introducing a two-parameter Tykhonov regularisation with a higher order L2 “viscosity term” for the $L^{\infty }$ L ∞ minimisation problem whi

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