Results 171 to 180 of about 36,597 (202)
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Local Well-Posedness for Fluid Interface Problems
Archive for Rational Mechanics and Analysis, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shatah, Jalal, Zeng, Chongchun
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Local well‐posedness of a critical inhomogeneous Schrödinger equation
Mathematical Methods in the Applied Sciences, 2022In this note, one studies the inhomogeneous Schrödinger equation Indeed, the local existence of solutions is established for a data , where and is the Sobolev critical exponent given by the equality . In particular, one considers the mass‐critical regime: and the energy critical regime: . In order to use Strichartz estimates without loss of
Tarek Saanouni, Congming Peng
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Local Well-Posedness and Regularity
2016In this chapter we study local well-posedness and regularity of the solutions of Problems (P1)~(P6). Here we employ without further comments the notations introduced in Chapters 1 and 2, in particular those in connection with Conditions (H1)~(H6) from Chapter 1, the Hanzawa transform, and the transformed problems on the fixed domain Ω\Σ in Section 1.3.
Jan Prüss, Gieri Simonett
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Local Well-Posedness and Continuation Criteria
2021The regularity theory for models with smooth communication is understandably quite different from singular models—the former is essentially Burgers’ equation with a damping mechanism, while the latter is a degenerate fractional parabolic system with dissipation in the momentum equation. In this chapter we will go through the first routine but very much
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Local Well-Posedness for the Einstein--Vlasov System
SIAM Journal on Mathematical Analysis, 2016The Vlasov equation gives a statistical description of a collection of some particles. It is characterized by the fact that there is no direct interaction between particles, i.e. no collisions are included in the model. The Vlasov equation can be coupled to the Einstein equations giving rise to the Einstein-Vlasov system. Solutions to this system model
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Local Well-posedness of Kinetic Chemotaxis Models
Journal of Evolution Equations, 2008We present a general functional analytic setting in which the Cauchy problem for mild solutions of kinetic chemotaxis models is well-posed, locally in time, in general physical dimensions. The models consist of a hyperbolic transport equation that is non-linearly and non-locally coupled to a reaction-diffusion system through kernel operators.
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Local well-posedness of a quasilinear wave equation
Applicable Analysis, 2015We study a quasilinear wave equation on a domain arising in nonlinear optics. We show local well-posedness for strong solutions using Kato’s approach to quasilinear evolution equations.
Dörfler, W. +2 more
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Local well-posedness for the homogeneous Euler equations
Nonlinear Analysis: Theory, Methods & Applications, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhong, Xin +2 more
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Local well-posedness of a new integrable equation
Nonlinear Analysis: Theory, Methods & Applications, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Yongqin, Wang, Weike
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On well-posedness of BVP in localization problems
Computer Methods in Applied Mechanics and Engineering, 1991Abstract Well-posedness of a BVP as equivalence problem of existence, uniqueness and stability of the BVP solution function is discussed. Some conditions which provide a unique and stable solution within hypoplasticity are presented. Several theoretical aspects that arise due to change of the type of the differential equation problem are studied.
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