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Relevant bibliographies by topics / Systems of Parabolic Equations

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Academic literature on the topic 'Systems of Parabolic Equations'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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Journal articles on the topic "Systems of Parabolic Equations"

1

Simon, László. "On some singular systems of parabolic functional equations." Mathematica Bohemica 135, no. 2 (2010): 123–32. http://dx.doi.org/10.21136/mb.2010.140689.

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Hrytchuk, M., and I. Klevchuk. "BIFURCATION OF TORI FOR PARABOLIC SYSTEMS OF DIFFERENTIAL EQUATIONS WITH WEAK DIFFUSION." Bukovinian Mathematical Journal 11, no. 2 (2023): 100–103. http://dx.doi.org/10.31861/bmj2023.02.10.

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The aim of the present article is to investigate of some properties of quasiperiodic solutions of nonlinear autonomous parabolic systems with the periodic condition. The research is devoted to the investigation of parabolic systems of differential equations with the help of integral manifolds method in the theory of nonlinear oscillations. We prove the existence of quasiperiodic solutions in autonomous parabolic system of differential equations with weak diffusion on the circle. We study existence and stability of an arbitrarily large finite number of tori for a parabolic system with weak diff

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Klevchuk, I. I. "Existence and stability of traveling waves in parabolic systems of differential equations with weak diffusion." Carpathian Mathematical Publications 14, no. 2 (2022): 493–503. http://dx.doi.org/10.15330/cmp.14.2.493-503.

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The aim of the present paper is to investigate of some properties of periodic solutions of a nonlinear autonomous parabolic systems with a periodic condition. We investigate parabolic systems of differential equations using an integral manifolds method of the theory of nonlinear oscillations. We prove the existence of periodic solutions in an autonomous parabolic system of differential equations with weak diffusion on the circle. We study the existence and stability of an arbitrarily large finite number of cycles for a parabolic system with weak diffusion. The periodic solution of parabolic eq

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Amann, Herbert. "Quasilinear evolution equations and parabolic systems." Transactions of the American Mathematical Society 293, no. 1 (1986): 191. http://dx.doi.org/10.1090/s0002-9947-1986-0814920-4.

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Kozhevnikov, A. "Multi–Weighted Parabolic Equations and Systems." Journal of Mathematical Sciences 193, no. 2 (2013): 267–82. http://dx.doi.org/10.1007/s10958-013-1452-0.

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Liu, Xingyu. "A System of Parabolic Laplacian Equations That Are Interrelated and Radial Symmetry of Solutions." Symmetry 17, no. 7 (2025): 1112. https://doi.org/10.3390/sym17071112.

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We utilize the moving planes technique to prove the radial symmetry along with the monotonic characteristics of solutions for a system of parabolic Laplacian equations. In this system, the solutions of the two equations are interdependent, with the solution of one equation depending on the function of the other. By use of the maximal regularity theory that has been established for fractional parabolic equations, we ensure the solvability of these systems. Our initial step is to formulate a narrow region principle within a parabolic cylinder. This principle serves as a theoretical basis for imp

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Al-Sultani, Mohamed Saleh Mehdi, and Igor Boglaev. "Block monotone iterations for solving coupled systems of nonlinear parabolic equations." ANZIAM Journal 61 (July 28, 2020): C166—C180. http://dx.doi.org/10.21914/anziamj.v61i0.15144.

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The article deals with numerical methods for solving a coupled system of nonlinear parabolic problems, where reaction functions are quasi-monotone nondecreasing. We employ block monotone iterative methods based on the Jacobi and Gauss–Seidel methods incorporated with the upper and lower solutions method. A convergence analysis and the theorem on uniqueness of a solution are discussed. Numerical experiments are presented. References Al-Sultani, M. and Boglaev, I. ''Numerical solution of nonlinear elliptic systems by block monotone iterations''. ANZIAM J. 60:C79–C94, 2019. doi:10.21914/anziamj.v

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Omuraliev, Asan, and Ella Abylaeva. "Regularized asymptotics of the solution of systems of parabolic differential equations." Filomat 36, no. 16 (2022): 5591–602. http://dx.doi.org/10.2298/fil2216591o.

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The regularization method for singularly perturbed problems of S. A. Lomov is generalized to constructing the asymptotics of the solution of the first boundary value problem for systems of differential equations of parabolic type with a small parameter at all derivatives.It is shown that the asymptotics of the solution of the problem contains n exponential, 2n parabolic and 2n angle boundary layer functions. The exponential boundary layer function describes the boundary layer along t = 0, the boundary layer along x = 0 and x = 1 is described by parabolic boundary layer functions.

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Kurima, Shunsuke. "Time discretization of an abstract problem from linearized equations of a coupled sound and heat flow." Electronic Journal of Differential Equations 2020, no. 01-132 (2020): 96. http://dx.doi.org/10.58997/ejde.2020.96.

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Recently, a time discretization of simultaneous abstract evolution equations applied to parabolic-hyperbolic phase-field systems has been studied. This article focuses on a time discretization of an abstract problem that has application to linearized equations of coupled sound and heat flow. As examples, we also study some parabolic-hyperbolic phase-field systems. For more information see https://ejde.math.txstate.edu/Volumes/2020/96/abstr.html

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Kavian, Otared, and Luz de Teresa. "Unique continuation principle for systems of parabolic equations." ESAIM: Control, Optimisation and Calculus of Variations 16, no. 2 (2009): 247–74. http://dx.doi.org/10.1051/cocv/2008077.

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Dissertations / Theses on the topic "Systems of Parabolic Equations"

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Crooks, Elaine Craig Mackay. "Travelling-wave solutions for parabolic systems." Thesis, University of Bath, 1996. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319218.

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Yolcu, Türkay. "Parabolic systems and an underlying Lagrangian." Diss., Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29760.

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In this thesis, we extend De Giorgi's interpolation method to a class of parabolic equations which are not gradient flows but possess an entropy functional and an underlying Lagrangian. The new fact in the study is that not only the Lagrangian may depend on spatial variables, but also it does not induce a metric. Assuming the initial condition is a density function, not necessarily smooth, but solely of bounded first moments and finite "entropy", we use a variational scheme to discretize the equation in time and construct approximate solutions. Moreover, De Giorgi's interpolation method is rev

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Yolcu, Türkay. "Parabolic systems and an underlying Lagrangian." Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29760.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010.<br>Committee Chair: Gangbo, Wilfrid; Committee Member: Chow, Shui-Nee; Committee Member: Harrell, Evans; Committee Member: Swiech, Andrzej; Committee Member: Yezzi, Anthony Joseph. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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Reichelt, Sina. "Two-scale homogenization of systems of nonlinear parabolic equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17385.

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Ziel dieser Arbeit ist es zwei verschiedene Klassen von Systemen nichtlinearer parabolischer Gleichungen zu homogenisieren, und zwar Reaktions-Diffusions-Systeme mit verschiedenen Diffusionslängenskalen und Gleichungen vom Typ Cahn-Hilliard. Wir betrachten parabolische Gleichungen mit periodischen Koeffizienten, wobei die Periode dem Verhältnis der charakteristischen mikroskopischen zu der makroskopische Längenskala entspricht. Unser Ziel ist es, effektive Gleichungen rigoros herzuleiten, um die betrachteten Systeme besser zu verstehen und den Simulationsaufwand zu minimieren. Wir suchen a

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Liu, Weian, Yin Yang, and Gang Lu. "Viscosity solutions of fully nonlinear parabolic systems." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2621/.

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In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].

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Floater, Michael S. "Blow-up of solutions to nonlinear parabolic equations and systems." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235037.

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Chen, Mingxiang. "Structural stability of periodic systems." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/29341.

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Floridia, Giuseppe. "Approximate multiplicative controllability for degenerate parabolic problems and regularity properties of elliptic and parabolic systems." Doctoral thesis, Università di Catania, 2012. http://hdl.handle.net/10761/1051.

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This thesis consists of two parts, both related to the theory of parabolic equations and systems. The first part is devoted to control theory which studies the possibility of influencing the evolution of a given system by an external action called control. Here we address approximate controllability problems via multiplicative controls, motivated by our interest in some differential models for the study of climatology. In the second part of the thesis we address regularity issues on the local differentiability and H\"older regularity for weak solutions of nonlinear systems in divergence form.

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Al, Refai Mohammed. "Sequential eigenfunction expansion for certain non-linear parabolic systems and wave type equations." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=36747.

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In trying to solve nonlinear partial differential equations with time dependence using the Galerkin method, one ends up with solving nonlinear systems of ordinary differential equations, which are not easily solved. In this thesis we introduce a new iterative method based on eigenfunction expansion to deal with the finite non-linear systems sequentially.<br>We apply the new method to integrate the semi-linear parabolic equation ut=12u+fu ,x∈D with homogeneous Dirichlet or Robin boundary conditions. We prove the convergence of the new iterative method, and use it to find the multiple solut

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Zhao, Yaxi. "Numerical solutions of nonlinear parabolic problems using combined-block iterative methods /." Electronic version (PDF), 2003. http://dl.uncw.edu/etd/2003/zhaoy/yaxizhao.pdf.

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Books on the topic "Systems of Parabolic Equations"

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Zheng, Songmu. Nonlinear parabolic equations and hyperbolic-parabolic coupled systems. Longman, 1995.

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Zheng, S. Nonlinear parabolic equations and hyperbolic-parabolic coupled systems. Longman, 1995.

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I, Volʹpert A. Traveling wave solutions of parabolic systems. American Mathematical Society, 1994.

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I, Koshelev A. Regularity problem for quasilinear elliptic and parabolic systems. Springer, 1995.

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Gastaldi, Fabio. On the coupling of hyperbolic and parabolic systems: Analytical and numerical approach. ICASE, 1988.

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Alfio, Quarteroni, and Langley Research Center, eds. On the coupling of hyperbolic and parabolic systems: Analytical and numerical approach. National Aeronautics and Space Administration, Langley Research Center, 1989.

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7

Smyshlyaev, Andrey. Adaptive control of parabolic PDEs. Princeton University Press, 2010.

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Smyshlyaev, Andrey. Adaptive control of parabolic PDEs. Princeton University Press, 2010.

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9

Qin, Yuming. Global Well-posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems. Springer Basel, 2012.

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10

Neittaanmäki, P. Optimal control of nonlinear parabolic systems: Theory, algorithms, and applications. M. Dekker, 1994.

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Book chapters on the topic "Systems of Parabolic Equations"

1

Banks, H. T., and K. Kunisch. "Parabolic Equations." In Estimation Techniques for Distributed Parameter Systems. Birkhäuser Boston, 1989. http://dx.doi.org/10.1007/978-1-4612-3700-6_5.

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Kavdia, Mahendra. "Parabolic Differential Equations, Diffusion Equation." In Encyclopedia of Systems Biology. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_273.

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Wang, Mingxin. "Weakly Coupled Parabolic Systems." In Nonlinear Second Order Parabolic Equations. CRC Press, 2021. http://dx.doi.org/10.1201/9781003150169-4.

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4

Rozovskii, B. L. "Ito’s Second Order Parabolic Equations." In Stochastic Evolution Systems. Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-011-3830-7_4.

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Rozovsky, Boris L., and Sergey V. Lototsky. "Itô’s Second-Order Parabolic Equations." In Stochastic Evolution Systems. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94893-5_4.

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Smith, Hal. "Quasimonotone systems of parabolic equations." In Mathematical Surveys and Monographs. American Mathematical Society, 2008. http://dx.doi.org/10.1090/surv/041/07.

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Pao, C. V. "Systems with Nonlinear Boundary Conditions." In Nonlinear Parabolic and Elliptic Equations. Springer US, 1992. http://dx.doi.org/10.1007/978-1-4615-3034-3_9.

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Pao, C. V. "Coupled Systems of Reaction Diffusion Equations." In Nonlinear Parabolic and Elliptic Equations. Springer US, 1992. http://dx.doi.org/10.1007/978-1-4615-3034-3_8.

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Kochubei, Anatoly N. "Fractional-parabolic equations and systems. Cauchy problem." In Fractional Differential Equations, edited by Anatoly Kochubei and Yuri Luchko. De Gruyter, 2019. http://dx.doi.org/10.1515/9783110571660-007.

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Pao, C. V. "Applications of Coupled Systems to Model Problems." In Nonlinear Parabolic and Elliptic Equations. Springer US, 1992. http://dx.doi.org/10.1007/978-1-4615-3034-3_12.

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Conference papers on the topic "Systems of Parabolic Equations"

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Qin, Hao, and Xingqi Zhang. "Parabolic Equation-based Channel Model for RIS-aided Train Communication Systems." In 2024 Photonics & Electromagnetics Research Symposium (PIERS). IEEE, 2024. http://dx.doi.org/10.1109/piers62282.2024.10618129.

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Arkhipova, Arina. "New a priori estimates for nondiagonal strongly nonlinear parabolic systems." In Parabolic and Navier–Stokes equations. Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-1.

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Zadrzyńska, Ewa, and Wojciech M. Zajączkowski. "Some linear parabolic system in Besov spaces." In Parabolic and Navier–Stokes equations. Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-36.

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Picard, Rainer. "The Stokes system in the incompressible case–revisited." In Parabolic and Navier–Stokes equations. Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-23.

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Cieślak, Tomasz, Philippe Laurençot, and Cristian Morales-Rodrigo. "Global existence and convergence to steady states in a chemorepulsion system." In Parabolic and Navier–Stokes equations. Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-7.

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Pawłow, Irena, and Wojciech M. Zajączkowski. "Global existence and uniqueness of weak solutions to Cahn-Hilliard-Gurtin system in elastic solids." In Parabolic and Navier–Stokes equations. Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-22.

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ARCEO, CARLENE P., JOSE MA L. ESCANER, MITSUHARU ÔTANI, and POLLY W. SY. "PARABOLIC EQUATIONS WITH SINGULARITY ON THE BOUNDARY." In Proceedings of Modelling and Control of Mechanical Systems. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776594_0002.

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Stańczy, Robert. "On radially symmetric solutions of some chemotaxis system." In Nonlocal and Abstract Parabolic Equations and their Applications. Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc86-0-19.

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Viglialoro, Giuseppe, Stella Vernier Piro, and Monica Marras. "Lower bounds for blow-up in a parabolic-parabolic Keller-Segel system." In The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Madrid, Spain). American Institute of Mathematical Sciences, 2015. http://dx.doi.org/10.3934/proc.2015.0809.

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Abels, Helmut. "Longtime behavior of solutions of a Navier-Stokes/Cahn-Hilliard system." In Nonlocal and Abstract Parabolic Equations and their Applications. Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc86-0-1.

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Reports on the topic "Systems of Parabolic Equations"

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Dalang, Robert C., and N. Frangos. Stochastic Hyperbolic and Parabolic Partial Differential Equations. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada290372.

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Rundell, William, and Michael S. Pilant. Undetermined Coefficient Problems for Quasi-Linear Parabolic Equations. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada256012.

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Nohel, John A. A Class of One-Dimensional Degenerate Parabolic Equations. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada160962.

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Dresner, L. On some general properties of parabolic conservation equations. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/10119060.

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Pilant, Michael S., and William Rundell. Undetermined Coefficient Problems for Quasi-Linear Parabolic Equations. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada218462.

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Ostashev, Vladimir, Michael Muhlestein, and D. Wilson. Extra-wide-angle parabolic equations in motionless and moving media. Engineer Research and Development Center (U.S.), 2021. http://dx.doi.org/10.21079/11681/42043.

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Wide-angle parabolic equations (WAPEs) play an important role in physics. They are derived by an expansion of a square-root pseudo-differential operator in one-way wave equations, and then solved by finite-difference techniques. In the present paper, a different approach is suggested. The starting point is an extra-wide-angle parabolic equation (EWAPE) valid for small variations of the refractive index of a medium. This equation is written in an integral form, solved by a perturbation technique, and transformed to the spectral domain. The resulting split-step spectral algorithm for the EWAPE a

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Carasso, Alfred S. Compensating Operators and Stable Backward in Time Marching in Nonlinear Parabolic Equations. National Institute of Standards and Technology, 2013. http://dx.doi.org/10.6028/nist.ir.7967.

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Hale, Jack K. Large Diffusivity and Asymptotic Behavior in Parabolic Systems. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada166197.

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Angenent, Sigurd. Parabolic Equations for Curves on Surfaces. 2. Intersections, Blow Up and Generalized Solutions. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada212890.

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Babuska, Ivo, and Tadeusz Janik. The p-Version of the Finite Element Method for Parabolic Equations. Part 1. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada197786.

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