Weighted Sobolev descent for singular first order partial differential equations.
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Well posed Cauchy problems for complex nonlinear equations must be semilinear.
Jorge Hounie, José R. dos Santos Filho (1992)
Mathematische Annalen
Well posedness and control of semilinear wave equations with iterated logarithms
Piermarco Cannarsa, Vilmos Komornik, Paola Loreti (1999)
ESAIM: Control, Optimisation and Calculus of Variations
Well posedness and control of semilinear wave equations with iterated logarithms
Piermarco Cannarsa, Vilmos Komornik, Paola Loreti (2010)
ESAIM: Control, Optimisation and Calculus of Variations
Motivated by a classical work of Erdős we give rather precise necessary and sufficient growth conditions on the nonlinearity in a semilinear wave equation in order to have global existence for all initial data. Then we improve some former exact controllability theorems of Imanuvilov and Zuazua.
Well posedness in for a weakly hyperbolic second order equation
Piero D'Ancona (1994)
Rendiconti del Seminario Matematico della Università di Padova
Well posedness under Levi conditions for a degenerate second order Cauchy problem
Alessia Ascanelli (2007)
Rendiconti del Seminario Matematico della Università di Padova
Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
Steve Bryson, Yekaterina Epshteyn, Alexander Kurganov, Guergana Petrova (2011)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples.
Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
Steve Bryson, Yekaterina Epshteyn, Alexander Kurganov, Guergana Petrova (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples.
Well-posedness and asynchronous exponential growth of solutions of a two-phase cell division model.
Bai, Meng, Cui, Shangbin (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain
Hans Zwart, Yann Le Gorrec, Bernhard Maschke, Javier Villegas (2010)
ESAIM: Control, Optimisation and Calculus of Variations
We study a class of hyperbolic partial differential equations on a one dimensional spatial domain with control and observation at the boundary. Using the idea of feedback we show these systems are well-posed in the sense of Weiss and Salamon if and only if the state operator generates a C0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.
Well-posedness and regularity results for a dynamic von Kármán plate.
Bradley, Mary E. (1995)
International Journal of Mathematics and Mathematical Sciences
Well-posedness in the Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time
F. Colombini, E. Jannelli, S. Spagnolo (1983)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Well-posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients
Ferruccio Colombini, Daniele del Santo, Tamotu Kinoshita (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
We prove that the Cauchy problem for a class of hyperbolic equations with non-Lipschitz coefficients is well-posed in and in Gevrey spaces. Some counter examples are given showing the sharpness of these results.
Well-posedness of the Cauchy problem for hyperbolic equations with non-Lipschitz coefficients.
Aliev, Akbar B., Shukurova, Gulnara D. (2009)
Abstract and Applied Analysis
Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds
Matania Ben-Artzi, Philippe G. Le Floch (2007)
Annales de l'I.H.P. Analyse non linéaire
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