Multi-dimensional scalar balance laws with discontinuous flux

We consider scalar balance laws with a dissipative source term. The flux function may be discontinuous with respect to both the space variable x and the unknown quantity u. We formulate the definition of entropy weak solutions and provide existence and uniqueness to the considered problem. The problem is formulated in the framework of multi-valued mappings. The notion of entropy measure-valued solutions is used to prove the so-called contraction principle and comparison principle.     

On uniqueness and existence of entropy solutions for a nonlinear parabolic problem with absorption

The aim of this paper is to study, for L ¹-data, the absorption problem of parabolic type : with Dirichlet boundary conditions and initial conditions. Here a satisfies the classical Leray-Lions hypotheses and β(x, ·) is the subdifferential ∂j(x, ·), where j is a convex function such that j(·, 0) = 0. Existence and uniqueness of an entropy solution is established.      

Renormalized solutions for nonlinear elliptic equations with variable exponents and L data

We prove existence and uniqueness of a renormalized solution to nonlinear elliptic equations with variable exponents and L¹$L^1$ data. The functional setting involves Lebesgue–Sobolev space with variable exponents W^1,p(⋅)(Ω)$W^{1,p(\cdot )}\left(\Omega \right)$.     

The Dirichlet problem for a conservation law with a multiplicative stochastic perturbation

In this paper, we are interested in the Dirichlet boundary value problem for a multi-dimensional nonlinear conservation law with a multiplicative stochastic perturbation. Using the concept of measure-valued solutions and Kruzhkov?s semi-entropy formulations, a result of existence and uniqueness of the entropy solution is proved.     

Renormalized solution for Stefan type problems: existence and uniqueness

We consider a class of nonlinear degenerate problems of Stefan type: $u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)$ where β is a maximal monotone graph in ${\mathbb{R}^2,}We consider a class of nonlinear degenerate problems of Stefan type:

ut- Dw -?F(u,w) = g(·,u),  w ? b(u)u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)      7. Renormalized solutions of nonlinear elliptic problems in generalized Orlicz spaces      Piotr Gwiazda  Petra Wittbold  Aneta Wróblewska  Aleksandra Zimmermann 《Journal of Differential Equations》2012,253(2):635-666       8. Purification and analysis of mono‐PEGylated HSA by hydrophobic interaction membrane chromatography      Xiaojiao Shang  William Wittbold  Raja Ghosh 《Journal of separation science》2013,36(23):3673-3681 We discuss the purification of mono‐PEGylated HSA by hydrophobic interaction membrane chromatography. The hydrophobicity difference between the different fractionated species was induced by the addition of a lyotropic salt that caused phase transition of PEG (hydrophilic under normal condition) to a mildly hydrophobic form. The HSA PEGylation reaction mixture was mixed with lyotropic salt and passed through a stack of hydrophilized polyvinylidene fluoride membrane discs. Unmodified HSA was obtained in the flow through, while the PEGylated forms of the protein bound to the membrane and could be eluted by reducing the salt concentration. Among the three major PEGylated forms of HSA present in the feed (i.e. mono–, di–, and tri–), mono‐PEGylated HSA was eluted first and could be resolved from the others. The purified material was analyzed by SDS‐PAGE, dynamic light scattering, and SEC combined with multi‐angle light scattering. All these analytical techniques indicated the presence of species that has a molar mass consistent with mono‐PEGylated HSA. A scaled‐down version of the membrane chromatographic methods could be used for the rapid and sensitive analysis of PEGylated proteins.      9. Quasi-linear parabolic problems in L 1 with non homogeneous conditions on the boundary      Kaouther Ammar  Petra Wittbold 《Journal of Evolution Equations》2005,5(1):1-33 We are interested in parabolic problems with L1 data of the type with i, j=0, 1, (i, j) (0, 0), 0 = 0 and 1 = 1. Here, is an open bounded subset of with regular boundary and is a Caratheodory function satisfying the classical Leray-Lions conditions and is a monotone graph in with closed domain and such that We study these evolution problems from the point of view of semi-group theory, then we identify the generalized solution of the associated Cauchy problem with the entropy solution of in the usual sense introduced in [5].      10. Corrigendum to “Renormalized solutions of nonlinear elliptic problems in generalized Orlicz spaces” [J. Differential Equations 253 (2) (2012) 635–666]      Piotr Gwiazda  Petra Wittbold  Aneta Wróblewska-Kamińska  Aleksandra Zimmermann 《Journal of Differential Equations》2012,253(9):2734-2738       1 [2] 下一页 » 末  页»

Purification and analysis of mono‐PEGylated HSA by hydrophobic interaction membrane chromatography

We discuss the purification of mono‐PEGylated HSA by hydrophobic interaction membrane chromatography. The hydrophobicity difference between the different fractionated species was induced by the addition of a lyotropic salt that caused phase transition of PEG (hydrophilic under normal condition) to a mildly hydrophobic form. The HSA PEGylation reaction mixture was mixed with lyotropic salt and passed through a stack of hydrophilized polyvinylidene fluoride membrane discs. Unmodified HSA was obtained in the flow through, while the PEGylated forms of the protein bound to the membrane and could be eluted by reducing the salt concentration. Among the three major PEGylated forms of HSA present in the feed (i.e. mono–, di–, and tri–), mono‐PEGylated HSA was eluted first and could be resolved from the others. The purified material was analyzed by SDS‐PAGE, dynamic light scattering, and SEC combined with multi‐angle light scattering. All these analytical techniques indicated the presence of species that has a molar mass consistent with mono‐PEGylated HSA. A scaled‐down version of the membrane chromatographic methods could be used for the rapid and sensitive analysis of PEGylated proteins.     

Quasi-linear parabolic problems in L 1 with non homogeneous conditions on the boundary

We are interested in parabolic problems with L¹ data of the type