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Nonlinear coupled system in thin domains with corrugated boundaries for metabolic processes
In this paper, we study the asymptotic behaviour of solutions of a coupled system of partial differential equations in a thin domain with oscillating...
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Solving nonlinear vectorial problems with a stable class of Jacobian-free iterative processes
In this manuscript, a general class of Jacobian-free iterative schemes for solving systems of nonlinear equations is presented. Once its fourth-order...
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Entrance Laws for Continuous-State Nonlinear Branching Processes Coming Down from Infinity
We consider a class of non-negative valued, time-changed spectrally positive Lévy processes stopped whenever hitting 0, which can be identified as...
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Markov Processes Associated with Nonlinear Fokker–Planck Equations
In this chapter, one presents an introductory treatment on McKean-Vlasov stochastic differential equations and their relationship with Fokker-Planck...
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Quality-Related Complex Nonlinear Process Monitoring
Nonlinear process is a common phenomenon in industrial processes, which shows a nonlinear relationship between the variables. Generally, PLS and its...
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Limit theorems of SDEs driven by Lévy processes and application to nonlinear filtering problems
In this paper we study the convergence of solutions for (possibly degenerate) stochastic differential equations driven by Lévy processes, when the...
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Computer Simulation System for Nonlinear Processes Described By the Korteweg–de Vries–Burgers Equation
The article discusses the computer simulation system for nonlinear processes described by the Korteweg–de Vries–Burgers equation. The Korteweg–de...
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Boundary Behaviors for a Continuous-state Nonlinear Neveu’s Branching Process
By generalizing a criterion of Mufa Chen for Markov jump processes, we establish the necessary and sufficient conditions for the extinction,...
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Nonlinear non-local multicontinua upscaling
In the past, many well-known linear and nonlinear upscaling tools have been developed, as mentioned earlier. Single-phase upscaling methods include...
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Hybrid Gaussian/Non-Gaussian Quality-Related Nonlinear Process Monitoring
In complex industrial processes, the mixed characteristics of Gaussian/non-Gaussian and nonlinear data are a common phenomenon. This process is...
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Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts
This book delves into a rigorous mathematical exploration of the well-posedness and long-time behavior of weak solutions to nonlinear Fokker-Planck...
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Conditional Gaussian Nonlinear Systems
In this chapter, a nonlinear modeling framework, called the conditional Gaussian nonlinear system (CGNS), is introduced. The CGNS contains a rich...
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An Algorithm for Decomposition Control and Prediction of Trajectories of Nonlinear Stochastic Systems Under Different-Speed Processes in Their Dynamics
The author proposes a decomposition algorithm for predicting the trajectories of nonlinear stochastic systems whose dynamics contain subprocesses...
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Fully Nonlinear Equations
In this chapter, we develop the theory of fully nonlinear nonlocal elliptic equations. We begin with the definition of viscosity solutions and their...
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The Cauchy Problem for a Doubly Nonlinear Parabolic Equation with Variable Density and Nonlinear Time-Dependent Absorption
Based on a self-similar analysis of the Fujita type global solvability, we obtain estimates for a solution and fronts (a free boundary) of the Cauchy...
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Stochastic Model of the Cauchy–Neumann Problem for Nonlinear Parabolic Equations
Stochastic equations are derived to describe reflected diffusion processes associated with the Cauchy–Neumann problem for nonlinear parabolic...
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Novel analysis of nonlinear seventh-order fractional Kaup–Kupershmidt equation via the Caputo operator
In this work, we use two unique methodologies, the homotopy perturbation transform method and Yang transform decomposition method, to solve the...
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Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to...
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Optimal Parameter Estimation Techniques for Complex Nonlinear Systems
Accurate parameter estimation and state identification within nonlinear systems are fundamental challenges addressed by optimization techniques. This...
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Lie–Bäcklund Symmetry, Reduction, and Solutions of Nonlinear Evolutionary Equations
We study the problem of symmetry reduction of nonlinear partial differential equations used to describe diffusion processes in an inhomogeneous...