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Quasi linear SPDEs in divergence form

Quasi linear SPDEs in divergence form

We develop a solution theory in Hölder spaces for a quasi-linear stochastic PDE driven by an additive noise. The key ingredients are two deterministic PDE lemmas which establish a priori Hölder bounds for a parabolic equation in divergence form with irregular right-hand-side term. We apply these bounds to the case of a right-hand- side noise term which is white in time and trace class in space, to obtain stretched exponential bounds for the Hölder semi-norms of the solution.

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To the Properties of the Solutions of a Cross diffusion Parabolic System not in Divergence Form

To the Properties of the Solutions of a Cross diffusion Parabolic System not in Divergence Form

Abstract The Zeldovich-Barenblatt type solution of the Cauchy problem for a cross-diffusion parabolic system not in divergence form with a source and a variable density is obtained. Based on comparison method the property of finite speed perturbation of distribution is considered. An asymptotic behavior of self-similar solutions, both for slow and fast diffusion cases, is established. It is obtained the system of the nonlinear algebraic equations with the coefficients of the main terms of the asymptotical solution.

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Maximum principles for a class of nonlinear second-order elliptic boundary value problems in divergence form

Maximum principles for a class of nonlinear second-order elliptic boundary value problems in divergence form

Philippin, Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature , Nonlinear Anal[r]

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Eigenvalue inequalities of elliptic operators in weighted divergence form on smooth metric measure spaces

Eigenvalue inequalities of elliptic operators in weighted divergence form on smooth metric measure spaces

on Riemannian manifolds, we refer to [–] and the references therein. As briefly men- tioned above, it is a natural problem how to get the universal inequalities of the eigenvalues of elliptic operator in weighted divergence form. Actually, in this paper, we first consider the eigenvalue problem as follows:

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Finite Speed of the Perturbation Distribution and Asymptotic Behavior of the Solutions of a Parabolic System not in Divergence Form

Finite Speed of the Perturbation Distribution and Asymptotic Behavior of the Solutions of a Parabolic System not in Divergence Form

Programs for the numerical solution of nonlinear systems not in divergence form developed in MATLAB. Programs are compact. By the user is entered the necessary numerical parameters. At the end of the file automatically displays the calculated results in the form of matrices and graphic. In the same place by running animation can trace the evolution of the process in time.

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Subsolutions of Elliptic Operators in Divergence Form and Application to Two-Phase Free Boundary Problems

Subsolutions of Elliptic Operators in Divergence Form and Application to Two-Phase Free Boundary Problems

precisely the subject of this paper. Once again, the key point is the construction of the previously mentioned family of subsolutions. Unlike the case of nondivergence or fully nonlinear operators, in the case of divergence form operators, the construction turns out to be rather delicate due to the fact that in this case not only the quadratic part of a function controls in average the action of the operator but also the linear part has an equivalent influence. Here we require Lipschitz continuous coefficients.

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Differential equations of divergence form in separable Musielak-Orlicz-Sobolev spaces

Differential equations of divergence form in separable Musielak-Orlicz-Sobolev spaces

method for differential equations of divergence form to prove the existence of weak so- lutions for (.) with Dirichlet boundary or Neumann boundary condition in separable Musielak-Orlicz-Sobolev spaces. We give the enclosure of weak solutions between sub- and supersolutions by using a sub-supersolution method. Our method does not require any monotonicity or coercivity of a  . We point out that the coercive condition (.) of

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A doubly degenerate diffusion equation not in divergence form with gradient term

A doubly degenerate diffusion equation not in divergence form with gradient term

Wang, J: Behaviors of solutions to a class of nonlinear degenerate parabolic equations not in divergence form. Winkler, M: Lager time behavior of solutions to degenerate parabolic equati[r]

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Dirichlet problem for divergence form elliptic equations with discontinuous coefficients

Dirichlet problem for divergence form elliptic equations with discontinuous coefficients

We study the Dirichlet problem for linear elliptic second order partial differential equations with discontinuous coefficients in divergence form in unbounded domains. We establish an existence and uniqueness result and we prove an a priori bound in L p , p > 2.

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To The Qualitative Properties Of Solution Of System Equations Not In Divergence Form

To The Qualitative Properties Of Solution Of System Equations Not In Divergence Form

are studied. In this work used: method of nonlinear splitting, known previously for non-linear parabolic equations and systems of equations in divergence form, asymptotic theory and asymptotic methods based on different transformations. Constructed asymptotic representation of self-similar solutions of nonlinear parabolic systems of equations not in divergence form, depending on the value in the system of the numerical parameters necessary and sufficient signs of their existence. The main purpose of this paper is to find conditions for the existence and non-existence results for global solutions of parabolic equations not in divergence form on the basis of the self-similar analysis. Keywords nonlinear parabolic systems of equations, not in divergence form, global solutions, self-similar solutions, asymptotic representation of solution
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An H1 Galerkin method for a Stefan problem with a quasilinear parabolic equation in non divergence form

An H1 Galerkin method for a Stefan problem with a quasilinear parabolic equation in non divergence form

A Galerkin Method For a Single Phase Nonlinear Stefan Problem with Dirichlet Boundary Conditions, Submitted.. Free-Boundary Problems For Nonlinear Parabolic Equations With Nonlinear Free[r]

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Uniqueness of weak solution for nonlinear elliptic equations in divergence form

Uniqueness of weak solution for nonlinear elliptic equations in divergence form

In this paper, we demonstrate the uniqueness of weak solution of the Dirichlet problem for divergence structure elliptic equations of the form.. Here, we consider the same problem for we[r]

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Existence of solutions for quasilinear elliptic systems in divergence form with variable growth

Existence of solutions for quasilinear elliptic systems in divergence form with variable growth

This paper is organized as follows: In Section , several important properties on variable exponent spaces are presented; in Section , we give some conclusions concerned with the Young [r]

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Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization

Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization

Abstract. We establish quantitative results on the periodic approximation of the corrector equation for the stochastic homogenization of linear elliptic equations in divergence form, when the diffusion coefficients satisfy a spectral gap estimate in probability, and for d > 2. This work is based on [5], which is a complete continuum version of [6, 7] (with in addition optimal results for d = 2). The main difference with respect to the first part of [5] is that we avoid here the use of Green’s functions and more directly rely on the De Giorgi-Nash-Moser theory.

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Quasilinear elliptic systems in perturbed form

Quasilinear elliptic systems in perturbed form

Hungerb¨ uhler, Quasilinear elliptic systems in divergence form with weak monotonicity, New York J.. Hungerb¨ uhler, Young Measures and Nonlinear PDEs, Habilitationsschrift, ETH Z¨ rich,[r]

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Global Existence and Blow-Up of Solutions for a Quasilinear Parabolic Equation with Absorption and Nonlinear Boundary Condition

Global Existence and Blow-Up of Solutions for a Quasilinear Parabolic Equation with Absorption and Nonlinear Boundary Condition

Li, Global existence and blow-up phenomena for nonlinear divergence form parabolic equations with inhomogeneous Neumann boundary conditions , J.. Liu and C.H.[r]

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Global existence and asymptotic behavior of solutions to a semilinear parabolic equation on Carnot groups

Global existence and asymptotic behavior of solutions to a semilinear parabolic equation on Carnot groups

a trivial Carnot group. In the Euclidean case, we first recall that Zhang [] studied the global existence for a parabolic problem in divergence form analogous to (.) when the potential V is in parabolic Kato class at infinity P ∞ , the asymptotic behavior of solutions for the problem was studied by Zhang and Zhao []. Riahi [] extended the results in []

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Uniqueness results for the Dirichlet problem for higher order elliptic equations in polyhedral angles

Uniqueness results for the Dirichlet problem for higher order elliptic equations in polyhedral angles

We consider the Dirichlet boundary value problem for higher order elliptic equations in divergence form with discontinuous coefficients in polyhedral angles!. Some uniqueness results are p[r]

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New information inequalities on new f  divergence by using ostrowski’s inequalities and its application

New information inequalities on new f divergence by using ostrowski’s inequalities and its application

Divergence measures have been demonstrated very useful in a variety of disciplines such as economics and political science (Gokhale and Kullback, 1978), ), signal processing (Kadota and (Bassat, 1978; Chen, 1973 and Jones and Byrne, 1990), color image (Taskar et al., 2006), cost- sensitive , magnetic resonance image analysis (Vemuri et al., 2010) etc. Also we can use divergences in fuzzy mathematics as fuzzy directed divergences and fuzzy entropies (Bajaj and Hooda, 2010;

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A non symmetric divergence and kullback leibler divergence measure

A non symmetric divergence and kullback leibler divergence measure

In whole paper, in the section 2, we have introduced information inequalities. New non-symmetric information divergence measure has derived in section 3. Bounds of new information divergence measure in terms of Kullback-Leibler divergence measure have studied in section 4. In section 5, give the numerical bounds of new non-symmetric information divergence in terms of Kullback-Leibler divergence measure.

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