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Relevant bibliographies by topics / Nonlinear PDE`s

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Journal articles

Academic literature on the topic 'Nonlinear PDE`s'

Author: Grafiati

Published: 18 May 2024

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Journal articles on the topic "Nonlinear PDE`s"

1

Khodja, Brahim. "A nonexistence result for a nonlinear PDE with Robin condition." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–12. http://dx.doi.org/10.1155/ijmms/2006/62601.

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Under the assumptionλ>0andfverifyingf(x,y,0)=0inD,2F(x,y,u)−uf(x,y,u)≥0,u≠0, and ifΩ=R×D, we show the convexity of functionE(t)=∬D|u(t,x,y)|2dxdy, whereu:Ω→ℝis a solution of problemλ(∂2u/∂t2)−(∂/∂x)(p(x,y)(∂u/∂x))−(∂/∂y)(q(x,y)(∂u/∂y))+f(x,y,u)=0 in Ω,u+ε(∂u/∂n)=0 on ∂Ω, considered inH2(Ω)∩L∞(Ω),p,q:D¯→ℝare two nonnull functions onD,εis a positive real number, andD=]a1,b1[×]a2,b2[,(F(x,y,s)=∫0sf(x,y,t)dt).

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2

Geldhauser, Carina, and Enrico Valdinoci. "Optimizing the Fractional Power in a Model with Stochastic PDE Constraints." Advanced Nonlinear Studies 18, no. 4 (2018): 649–69. http://dx.doi.org/10.1515/ans-2018-2031.

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AbstractWe study an optimization problem with SPDE constraints, which has the peculiarity that the control parameter s is the s-th power of the diffusion operator in the state equation. Well-posedness of the state equation and differentiability properties with respect to the fractional parameter s are established. We show that under certain conditions on the noise, optimality conditions for the control problem can be established.

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3

Ji, Binxin, Xiangxing Tao, and Yanting Ji. "Barrier Option Pricing in the Sub-Mixed Fractional Brownian Motion with Jump Environment." Fractal and Fractional 6, no. 5 (2022): 244. http://dx.doi.org/10.3390/fractalfract6050244.

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This paper investigates the pricing formula for barrier options where the underlying asset is driven by the sub-mixed fractional Brownian motion with jump. By applying the corresponding Ito^’s formula, the B-S type PDE is derived by a self-financing strategy. Furthermore, the explicit pricing formula for barrier options is obtained through converting the PDE to the Cauchy problem. Numerical experiments are conducted to test the impact of the barrier price, the Hurst index, the jump intensity and the volatility on the value of barrier option respectively.

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4

KNESSL, CHARLES. "Asymptotic analysis of the American call option with dividends." European Journal of Applied Mathematics 13, no. 6 (2002): 587–616. http://dx.doi.org/10.1017/s0956792502004898.

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We consider an American call option and let C(S, T0) be the price of an option corresponding to asset price S at some time T0 prior to the expiration time TF . We analyze C(S, T0) in various asymptotic limits. These include situations where the interest and dividend rates are large or small, compared to the volatility of the asset. We also analyze the optimal exercise boundary for the option. We use perturbation methods to analyze either the PDE that C(S, T0) satisfies, or a nonlinear integral equation that is satisfied by the optimal exercise boundary.

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5

Philippin, G. A., and A. Safoui. "Some applications of the maximum principle to a variety of fully nonlinear elliptic PDE?s." Zeitschrift f�r Angewandte Mathematik und Physik (ZAMP) 54, no. 5 (2003): 739–55. http://dx.doi.org/10.1007/s00033-003-3200-7.

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6

Bonazebi-Yindoula, Joseph. "Laplace-SBA Method for Solving Nonlinear Coupled Burger's Equations." European Journal of Pure and Applied Mathematics 14, no. 3 (2021): 842–62. http://dx.doi.org/10.29020/nybg.ejpam.v14i3.3932.

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Burgerâ€™s equations, an extension of fluid dynamics equations, are typically solved by several numerical methods. In this article, the laplace-SomÃ© Blaise Abbo method is used to solve nonlinear Burger equations. This method is based on the combination of the laplace transform and the SBA method. After reminders of the laplace transform, the basic principles of the SBA method are described. The process of calculating the Laplace-SBA algorithm for determining the exact solution of a linear or nonlinear partial derivative equation is shown. Thus, three examplesof PDE are solved by this method,

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7

Cavalcanti, Marcelo M., Valéria N. Domingos Cavalcanti, Irena Lasiecka, and Claudete M. Webler. "Intrinsic decay rates for the energy of a nonlinear viscoelastic equation modeling the vibrations of thin rods with variable density." Advances in Nonlinear Analysis 6, no. 2 (2017): 121–45. http://dx.doi.org/10.1515/anona-2016-0027.

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AbstractWe consider the long-time behavior of a nonlinear PDE with a memory term which can be recast in the abstract form$\frac{d}{dt}\rho(u_{t})+Au_{tt}+\gamma A^{\theta}u_{t}+Au-\int_{0}^{t}g(s)Au(t% -s)=0,$where A is a self-adjoint, positive definite operator acting on a Hilbert space H, ${\rho(s)}$ is a continuous, monotone increasing function, and the relaxation kernel ${g(s)}$ is a continuous, decreasing function in ${L_{1}(\mathbb{R}_{+})}$ with ${g(0)>0}$. Of particular interest is the case when ${A=-\Delta}$ with appropriate boundary conditions and ${\rho(s)=|s|^{\rho}s}$. This mod

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8

Bridges, Thomas J. "Canonical multi-symplectic structure on the total exterior algebra bundle." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2069 (2006): 1531–51. http://dx.doi.org/10.1098/rspa.2005.1629.

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The aim of this paper is to construct multi-symplectic structures starting with the geometry of an oriented Riemannian manifold, independent of a Lagrangian or a particular partial differential equation (PDE). The principal observation is that on an n -dimensional orientable manifold M there is a canonical quadratic form Θ associated with the total exterior algebra bundle on M . On the fibre, which has dimension 2 n , the form Θ can be locally decomposed into n classical symplectic structures. When concatenated, these n -symplectic structures define a partial differential operator, J ∂ , which

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9

Wei, Hongbo, Xuerong Cui, Yucheng Zhang, and Jingyao Zhang. "$ H_\infty $ deployment of nonlinear multi-agent systems with Markov switching topologies over a finite-time interval based on T–S fuzzy PDE control." AIMS Mathematics 9, no. 2 (2024): 4076–97. http://dx.doi.org/10.3934/math.2024199.

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<abstract><p>The deployment of multi-agent systems (MASs) is widely used in the fields of unmanned agricultural machineries, unmanned aerial vehicles, intelligent transportation, etc. To make up for the defect that the existing PDE-based results are overly idealistic in terms of system models and control strategies, we study the PDE-based deployment of clustered nonlinear first-order and second-order MASs over a finite-time interval (FTI). By designing special communication protocols, the collective dynamics of numerous agents are modeled by simple fist-order and second-order PDEs.

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10

Daoues, Adel, Amani Hammami, and Kamel Saoudi. "Multiple positive solutions for a nonlocal PDE with critical Sobolev-Hardy and singular nonlinearities via perturbation method." Fractional Calculus and Applied Analysis 23, no. 3 (2020): 837–60. http://dx.doi.org/10.1515/fca-2020-0042.

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AbstractIn this paper we investigate the following nonlocal problem with singular term and critical Hardy-Sobolev exponent$$\begin{array}{} ({\rm P}) \left\{ \begin{array}{ll} (-\Delta)^s u = \displaystyle{\frac{\lambda}{u^\gamma}+\frac{|u|^{2_\alpha^*-2}u}{|x|^\alpha}} \ \ \text{ in } \ \ \Omega, \\ u >0 \ \ \text{ in } \ \ \Omega, \quad u = 0 \ \ \text{ in } \ \ \mathbb{R}^{N}\setminus \Omega, \end{array} \right. \end{array}$$where Ω ⊂ ℝN is an open bounded domain with Lipschitz boundary, 0 < s < 1, λ > 0 is a parameter, 0 < α < 2s < N, 0 < γ < 1 < 2 < $\begi

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