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Showing 1 to 20 of 54 for “"nonlinear partial differential equations"”.
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Variational Methods for Nonlinear Partial Differential Equations
… of variational methods for solving a class of nonlinear partial differential equations. First, relevant mathematical background of functional analysis and variational calculus is explained. One of the main results discussed is the existence theorem for minimizer of functionals for the case of …
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Smoothing properties of certain dispersive nonlinear partial differential equations
… with the smoothing properties of dispersive equations and systems. Smoothing in this context means that the nonlinear part of the solution flow is of higher regularity than the initial data. We establish this property, and some of its consequences, for several equations. The first part of the …
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Optimal Control Problems Governed by Nonlinear Partial Differential Equations and Inclusions
… of optimal control problems constrained by nonlinear partial differential equations (PDE) and inclusions (PDI). There exist statements on the existence of solutions for optimal control problems with linear and semi-linear PDEs with monotone parts. The theory for non-monotone PDEs resp. the …
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Optimization Methods for Dynamic Mode Decomposition of Nonlinear Partial Differential Equations
… long been used to understand the behavior of nonlinear partial differential equations. Naturally, reduced-order modeling techniques come at the price of either computational accuracy or computation time. Optimization techniques are studied to improve either or both of these objectives and …
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On some nonlinear partial differential equations for classical and quantum many body systems
… deals with problems arising in the study of nonlinear partial differential equations arising from many-body problems. It is divided into two parts: The first part concerns the derivation of a nonlinear diffusion equation from a microscopic stochastic process. We give a new method to show that …
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Exact solutions and conservation laws of two-wave mode Kadomtsev-Petviashvili equation and a nonintegrable nonlinear equation
In this dissertation we study three nonlinear partial differential equations namely the Korteweg-de Vries (KdV) equation as an illustrative example, nonintegrable nonlinear equation and two-wave mode Kadomtsev-Petviashvili (TKP) equation. We employ the multiplier method to find conservation laws. …
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The evolution equation for closed magnetic geodesics
… They appear as solutions to a system of (nonlinear) ordinary differential equations of second order. But we are only interested in periodic solutions. To this end, we study the corresponding system of (nonlinear) parabolic equations for closed magnetic geodesics and, as a main result, …
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Exact coherent structures in spatiotemporal chaos: From qualitative description to quantitative predictions
… turbulence, where the motion is described by nonlinear partial differential equations. It is well known from the studies of low dimensional chaotic systems that the state space, the space of solutions to the governing dynamical equations, is shaped by the invariant sets such as equilibria, …
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Soliton Propagation in nonlinear optical fibers: theory and application
A survey of research in nonlinear optical fibers is given. Important background concepts are introduced and explained. Present and future applications of nonlinear optical fibers arc reviewed. A mathematical model of a nonlinear optical fiber is developed using a coupled-mode theory approach, and …
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Regularity results for some elliptic and parabolic problems
… thesis deals with the regularity of solutions to nonlinear partial differential equations of elliptic and parabolic type, and it collects some results obtained during the last three years under the supervision of Prof. Ugo Gianazza The first part concernes the study of singular porous medium type …
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Nonlinear Vibrations of Doubly Curved Cross-PLy Shallow Shells
… of this work is to study the local and global nonlinear vibrations of isotropic single-layered and multi-layered cross-ply doubly curved shallow shells with simply supported boundary conditions. The study is based-on the full nonlinear partial-differential equations of motion for shells. These …
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Mathematical theory of isoelectric focusing.
… ampholytes is proposed. The problem consists of nonlinear partial differential equations and algebraic equations under nonlinear boundary conditions. Different models of IEF have been studied. For each model problem, we investigated the qualitative properties such as the local existence, global …
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Deeply-towed underwater vehicle systems : a verified analytical procedure for creating parameterized dynamic models
… cable/vehicle systems are governed by nonlinear partial differential equations and as a result, trajectory control is generally difficult using the available techniques. This work examines the possibility of utilizing parametric dynamic models in differential equation form, to present a …
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Mathematical modelling of negative feedback signal transduction processes
… work, we derive mathematicalmodels (systems of partial differential equations) to capture the evolution in space and time of the key variables in the Hes1 and p53-Mdm2 systems. Computational simulations allow us to show that our reaction-diffusion models are able to produce sustained …
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Convergence of material balance in mathematical simulation of petroleum reservoirs
… of finite difference approximations to represent nonlinear partial differential equations.</p> <p>A new procedure called Error Matrix Technique has been developed for reduction of material balance errors. This reduction is accomplished by adjusting potential gradients at every grid point in the …
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Infinitely Many Solutions to Asymmetric, Polyharmonic Dirichlet Problems
… on the existence of infinitely many solutions to nonlinear partial differential equations that are perturbed from symmetry. Our main theorems focus on polyharmonic Dirichlet problems with exponential nonlinearities, and are now published in Topol. Methods Nonlinear Anal. Vol. 50, No.1, (2017), …
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The laminar boundary layer on spinning bodies of revolution
… dissertation is the analysis and solution of the equations describing the laminar boundary layer on axisymmetric bodies immersed in an oncoming stream and spinning at a constant rate about their axis of revolution. The flow is allowed to be compressible or incompressible and the geometries for …
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Qualitative Properties Of Solutions Of Fully Nonlinear Equations And Overdetermined Problems
… radial symmetry for viscosity solutions of fully nonlinear partial differential equations. We</p> <p>obtain the radial symmetry and monotonicity properties for</p> <p>nonnegative viscosity solutions of fully nonlinear equations under some asymptotic decay rate at infinity. Our symmetry and …
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Spectral stability of solutions to Whitham-type equations with a nonlocal kernel
… of finding travelling wave solutions to certain nonlinear partial differential equations. This is done using a spectral cosine collocation method, and the stability of the travelling wave solutions found is then assessed using the Fourier-Floquet-Hill method. This is first done on a number of …
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