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A well-posedness result for an extended KdV equation
Partial Differential Equations in Applied MathematicsAmong the most interesting things Russell discovered was there is a mathematical relation between the height of the wave, the depth of the wave when water at rest and the speed at which the wave travels.
M. Berjawi, T. El Arwadi, S. Israwi
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Acoustic waves interacting with non–locally reacting surfaces in a Lagrangian framework
Mathematische Nachrichten, Volume 298, Issue 12, Page 3855-3892, December 2025.Abstract The paper deals with a family of evolution problems arising in the physical modeling of small amplitude acoustic phenomena occurring in a fluid, bounded by a surface of extended reaction. They are all derived in a Lagrangian framework. We study well‐posedness of these problems, their mutual relations, and their relations with other evolution ...
Enzo Vitillaro
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Global well-posedness for the non-viscous MHD equations with magnetic diffusion in critical Besov spaces [PDF]
, 2021 Weikui Ye, Zhaoyang Yin
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Well-posedness of KdV type equations
Electronic Journal of Differential Equations, 2012 In this work, we study the initial value problems associated to some linear perturbations of KdV equations. Our focus is in the well-posedness issues for initial data given in the L^2-based Sobolev spaces.
Xavier Carvajal, Mahendra Panthee
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On the principle of linearized stability for quasilinear evolution equations in time‐weighted spaces
Mathematische Nachrichten, Volume 298, Issue 12, Page 3939-3959, December 2025.Abstract Quasilinear (and semilinear) parabolic problems of the form v′=A(v)v+f(v)$v^{\prime }=A(v)v+f(v)$ with strict inclusion dom(f)⊊dom(A)$\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ of the domains of the function v↦f(v)$v\mapsto f(v)$ and the quasilinear part v↦A(v)$v\mapsto A(v)$ are considered in the framework of time‐weighted function spaces ...
Bogdan‐Vasile Matioc +2 more
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Well-Posedness of History-Dependent Sweeping Processes
SIAM Journal on Mathematical Analysis, 2019 This paper is devoted to the study of a class of sweeping processes with history-dependent operators.
S. Migórski, M. Sofonea, Shengda Zeng
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Journal of Applied Mathematics, 2012 The purpose of this paper is to investigate the problems of the well-posedness for a system of mixed quasivariational-like inequalities in Banach spaces.
L. C. Ceng, Y. C. Lin
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 18, Page 16263-16289, December 2025.ABSTRACT In this study, we investigate the synergistic roles of adoptive T cell therapy (ACT), specifically using tumor‐infiltrating lymphocytes (TILs) and oncolytic virus (OV) therapy in enhancing cancer treatment efficacy. While OVs can initiate tumor destruction, they often fail to achieve complete tumor eradication or generate a strong antitumor ...
Salaheldin Omer +2 more
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Diffusive Resource–Consumer Dynamics With the Simplest Learning Mechanism and Nonlocal Memory Usage
Mathematical Methods in the Applied Sciences, Volume 48, Issue 18, Page 16433-16444, December 2025.ABSTRACT To describe cognitive consumers' movement, we study a diffusive resource–consumer model with nonlocal memory usage described by a system of parabolic equations, which is coupled with spatial memory dynamics described by a linear learning equation.
Qigang Deng, Ranchao Wu, Hao Wang
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Almost critical well-posedness for nonlinear wave equations with $Q_{\mu \nu}$ null forms in 2D [PDF]
, 2014 Viktor Grigoryan, Andrea R. Nahmod
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