Results 41 to 50 of about 11,044,020 (324)
Weak solutions to problems involving inviscid fluids
, 2015 We consider an abstract functional-differential equation derived from the pressure-less Euler system with variable coefficients that includes several systems of partial differential equations arising in the fluid mechanics.
C Audiard +14 more
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Dimensionalities of Weak Solutions in Hydrogenic Systems
, 2006 A close inspection on the 3D hydrogen atom Hamiltonian revealed formal eigenvectors often discarded in the literature. Although not in its domain, such eigenvectors belong to the Hilbert space, and so their time evolution is well defined.
+17 more
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On the Burgers-Poisson Equation [PDF]
, 2016 In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L^1(R). Additional an Oleinik type estimate is established and some criteria on local smoothness and wave breaking for weak
Grunert, Katrin, Nguyen, Khai T.
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The higher integrability of weak solutions of porous medium systems
Advances in Nonlinear Analysis, 2018 In this paper we establish that the gradient of weak solutions to porous medium-type systems admits the self-improving property of higher integrability.
V. Bögelein +3 more
semanticscholar +1 more source
Mathematical models for erosion and the optimal transportation of sediment
, 2013 We investigate a mathematical theory for the erosion of sediment which begins with the study of a non-linear, parabolic, weighted 4-Laplace equation on a rectangular domain corresponding to a base segment of an extended landscape.
Birnir, B., Rowlett, J.
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Global weak solutions and asymptotic limits of a Cahn--Hilliard--Darcy system modelling tumour growth [PDF]
, 2016 We study the existence of weak solutions to a Cahn--Hilliard--Darcy system coupled with a convection-reaction-diffusion equation through the fluxes, through the source terms and in Darcy's law.
H. Garcke, K. F. Lam
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Remark on regularity criteria of a weak solution to the 3D MHD equations
Electronic Journal of Qualitative Theory of Differential Equations, 2017 We study the regularity conditions for a weak solution to 3D MHD equations in a whole space $\mathbb{R}^3$, based on the papers [C. He, Y. Wang, J. Differential Equations, 238(2007), No. 1, 1–17] and [W. Wang, J. Math. Anal. Appl., 328(2007), No. 2, 1082–
Jae-Myoung Kim
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Mathematical Modelling and Analysis, 2022 A new variational approach for a boundary value problem in mathematical physics is proposed. By considering two-field Lagrange multipliers, we deliver a variational formulation consisting of a mixed variational problem which is equivalent with a saddle ...
Mariana Chivu Cojocaru, Andaluzia Matei
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Hamiltonian structure of peakons as weak solutions for the modified Camassa-Holm equation
, 2018 The modified Camassa-Holm (mCH) equation is a bi-Hamiltonian system possessing $N$-peakon weak solutions, for all $N\geq 1$, in the setting of an integral formulation which is used in analysis for studying local well-posedness, global existence, and wave
Anco, Stephen C., Kraus, Daniel
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Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions
Journal of elasticity, 2017 The well-posedness of the boundary value problems for second gradient elasticity has been studied under the assumption of strong ellipticity of the dependence on the second placement gradients (see, e.g., Chambon and Moullet in Comput. Methods Appl. Mech.
V. Eremeyev +3 more
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