Results 71 to 80 of about 18,044,700 (176)
On the well-posedness of global fully nonlinear first order elliptic systems
Advances in Nonlinear Analysis, 2018 In the very recent paper [15], the second author proved that for any f∈L2(ℝn,ℝN){f\in L^{2}(\mathbb{R}^{n},\mathbb{R}^{N})}, the fully nonlinear first order system F(⋅,Du)=f{F(\,\cdot\,,\mathrm{D}u)=f} is well posed in the so-called J. L.
Abugirda Hussien, Katzourakis Nikos
doaj +1 more source
Frequency‐dependent contraction rates for the Bayesian method to the inverse source problem
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract This paper addresses an inverse source problem for acoustic waves in a range of frequencies. Our study has two main goals. First, although the problem is severely ill‐posed with a logarithmic stability estimate, we demonstrate, through careful analysis of the forward map's singular values, that increasing the frequency range enhances stability,
Pu‐Zhao Kow, Jenn‐Nan Wang
wiley +1 more source
Global well-posedness for KdV in Sobolev spaces of negative index
Electronic Journal of Differential Equations, 2001 The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data.
James Colliander +4 more
doaj
Control Design Based on Generalized Lur'e Lyapunov Functions for Sampled‐Data Lur'e Systems
International Journal of Robust and Nonlinear Control, Volume 36, Issue 16, Page 7450-7463, 10 November 2026.ABSTRACT This article addresses the synthesis of stabilizing control laws for aperiodic sampled‐data Lur'e systems. Based on a hybrid system representation of the closed‐loop system and a timer‐dependent generalized Lur'e–Postnikov type Lyapunov function, stabilization conditions are obtained by separating decision variables with the application of two
Arthur Scolari Fagundes +2 more
wiley +1 more source
A Unified Block‐Modal Framework for Inverse Source Problems in Heat and Mass Transfer
International Journal for Numerical Methods in Engineering, Volume 127, Issue 19, 15 October 2026.ABSTRACT This work presents a unified block–modal framework for inverse source identification in linear diffusive problems arising in heat and mass transfer. Starting from a general parabolic model with mixed boundary operators, the Classical Integral Transform Technique is employed to project the dynamics onto an orthonormal eigenbasis, yielding a ...
André J. P. de Oliveira +5 more
wiley +1 more source
Applied Research, Volume 5, Issue 5, October 2026.This study introduces a structurally cascaded physics‐informed graph neural network to model tumor microenvironments accurately. By enforcing a directional dependency from mechanical strain to biochemical secretion, the method eliminates unphysical artifacts and significantly improves predictive accuracy for precision healthcare applications.
Xinyuan Chen +2 more
wiley +1 more source
A Test Function Method for Weakly Coupled Systems With Derivative‐Type Nonlinearity
Mathematische Nachrichten, Volume 299, Issue 10, Page 3015-3035, October 2026.ABSTRACT We consider a two by two system of inequalities which include fractional powers of the Laplace operator, coupled through a semilinear term of derivative type. We prove the nonexistence of global‐in‐time weak solutions for powers below the critical curve and possibly on the critical curve.
Marcello D'Abbicco, Antonio Lagioia
wiley +1 more source
Global well-posedness for nonlinear nonlocal Cauchy problems arising in elasticity
Electronic Journal of Differential Equations, 2017 In this article, we prove global well-posedness for a family of one dimensional nonlinear nonlocal Cauchy problems arising in elasticity. We consider the equation $$ u_{tt}-\delta Lu_{xx}=\big(\beta \ast [(1-\delta)u+u^{2n+1}]\big)_{xx}\,, $$ where
Hantaek Bae, Suleyman Ulusoy
doaj
A Model of Strategic Sustainable Investment
Mathematical Finance, Volume 36, Issue 4, Page 771-803, October 2026.ABSTRACT We study a problem of optimal irreversible investment and emission reduction formulated as a nonzero‐sum dynamic game between an investor with environmental preferences and a firm. The game is set in continuous‐time on an infinite‐time horizon.
Tiziano De Angelis +2 more
wiley +1 more source
Diophantine conditions in global well-posedness for coupled KdV-type systems
Electronic Journal of Differential Equations, 2009 We consider the global well-posedness problem of a one-parameter family of coupled KdV-type systems both in the periodic and non-periodic setting. When the coupling parameter $alpha = 1$, we prove the global well-posedness in $H^s(mathbb{R}) $ for $s >
Tadahiro Oh
doaj