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Displaying 21 – 34 of 34

On the local Cauchy problem for first order partial differential functional equations

Elżbieta Puźniakowska-Gałuch (2010)

Annales Polonici Mathematici

A theorem on the existence of weak solutions of the Cauchy problem for first order functional differential equations defined on the Haar pyramid is proved. The initial problem is transformed into a system of functional integral equations for the unknown function and for its partial derivatives with respect to spatial variables. The method of bicharacteristics and integral inequalities are applied. Differential equations with deviated variables and differential integral equations can be obtained...

On the Neumann problem with L¹ data

J. Chabrowski (2007)

Colloquium Mathematicae

We investigate the solvability of the linear Neumann problem (1.1) with L¹ data. The results are applied to obtain existence theorems for a semilinear Neumann problem.

On the regularity for solutions of the micropolar fluid equations

Elva Ortega-Torres, Marko Rojas-Medar (2009)

Rendiconti del Seminario Matematico della Università di Padova

On the singular behavior of solutions of a transmission problem in a dihedral.

Benseridi, H., Dilmi, M. (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

On the solvability of Dirichlet problem for the weighted p-Laplacian

Dominik Mielczarek, Jerzy Rydlewski, Ewa Szlachtowska (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we are concerned with the existence and uniqueness of the weak solution for the weighted p-Laplacian. The purpose of this paper is to discuss in some depth the problem of solvability of Dirichlet problem, therefore all proofs are contained in some detail. The main result of the work is the existence and uniqueness of the weak solution for the Dirichlet problem provided that the weights are bounded. Furthermore, under this assumption the solution belongs to the Sobolev space $W ₀^{1, p} (Ω)$ .

On the solvability of superlinear and nonhomogeneous quasilinear equations.

Jia, Gao, Zhao, Qing, Dai, Chun-Yan (2009)

Boundary Value Problems [electronic only]

On the solvability of the equation div $u = f$ in $L^{1}$ and in $C^{0}$

Bernard Dacorogna, Nicola Fusco, Luc Tartar (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We show that the equation div $u = f$ has, in general, no Lipschitz (respectively $W^{1, 1}$ ) solution if $f$ is $C^{0}$ (respectively $L^{1}$ ).

On the strong solution for the 3D stochastic Leray- $α$ model.

Deugoue, Gabriel, Sango, Mamadou (2010)

Boundary Value Problems [electronic only]

On the uniqueness of bounded weak solutions to the Navier-Stokes Cauchy problem

Paolo Maremonti (2009)

Matematički Vesnik

On the uniqueness of weak solutions for the 3D Navier-Stokes equations

Qionglei Chen, Changxing Miao, Zhifei Zhang (2009)

Annales de l'I.H.P. Analyse non linéaire

On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients

Petr Harasim (2011)

Applications of Mathematics

We apply a theoretical framework for solving a class of worst scenario problems to a problem with a nonlinear partial differential equation. In contrast to the one-dimensional problem investigated by P. Harasim in Appl. Math. 53 (2008), No. 6, 583–598, the two-dimensional problem requires stronger assumptions restricting the admissible set to ensure the monotonicity of the nonlinear operator in the examined state problem, and, as a result, to show the existence and uniqueness of the state solution....

On weak solutions of the equations of motion of a viscoelastic medium with variable boundary.

Zvyagin, V.G., Orlov, V.P. (2005)

Boundary Value Problems [electronic only]

On weak-strong uniqueness property for full compressible magnetohydrodynamics flows

Weiping Yan (2013)

Open Mathematics

This paper is devoted to the study of the weak-strong uniqueness property for full compressible magnetohydrodynamics flows. The governing equations for magnetohydrodynamic flows are expressed by the full Navier-Stokes system for compressible fluids enhanced by forces due to the presence of the magnetic field as well as the gravity and an additional equation which describes the evolution of the magnetic field. Using the relative entropy inequality, we prove that a weak solution coincides with the...

Optimal interior partial regularity for nonlinear elliptic systems for the case $1 < m < 2$ under natural growth condition.

Chen, Shuhong, Tan, Zhong (2010)

Journal of Inequalities and Applications [electronic only]

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