Cover Image

Boundedness of weak solutions of a nondiagonal singular parabolic system of three equations

The $L^{∞}$-estimates of weak solutions are established for a quasilinear nondiagonal parabolic system of singular equations whose matrix of coefficients satisfies special structural conditions. A procedure based on the estimation of linear combinations of the unknowns is used.

Saved in:

Bibliographic Details
Date:	2006
Main Authors:	Portnyagin, D. V., Понтрягин, Д. В.
Format:	Article
Language:	English
Published:	Institute of Mathematics, NAS of Ukraine 2006
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/3515
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

Boundedness of weak solutions of a nondiagonal singular parabolic system of three equations
by: Portnyagin, D.V.
Published: (2006)

Boundedness of weak solutions of a nondiagonal parabolic system of two equations
by: Portnyahin, D. V., et al.
Published: (2009)

Propagation of Singularities for Large Solutions of Quasilinear Parabolic Equations
by: Y. A. Yevgenieva
Published: (2019)

On some periodic solutions of singularly perturbed parabolic equations
by: Vasilyeva, A. B., et al.
Published: (2007)

Removable isolated singularities for solutions of quasilinear parabolic equations
by: Nicolosi, F., et al.
Published: (2009)

The decomposition of a solution of the quasilinear stochastic parabolic equation with weak source
by: Melnik, S.
Published: (2007)

Boundedness of solutions and asymptotic properties of some systems of differential equations
by: Gorodetskii, V. G., et al.
Published: (1994)

On the existence of initial values of solutions of weakly nonlinear parabolic equations
by: Skrypnik, I. I., et al.
Published: (1993)

One method for solution of the Cauchy problem for singular parabolic equations
by: Matiichuk , M. I., et al.
Published: (1992)

On the Boundedness of Singular Integral Operators in Symmetric Spaces
by: Peleshenko, B. I., et al.
Published: (2000)

$G$-convergence of parabolic operators and weak convergence of solutions of diffusion equations
by: Makhno, S. Ya., et al.
Published: (1993)

Boundedness of Solutions of Fractional-like Equations of Perturbed Motion
by: A. A. Martynjuk, et al.
Published: (2020)

Optimization of direct methods for the approximate solution of weakly singular integral equations
by: Urumbaev, A. N., et al.
Published: (1994)

Stefan problem for a weakly degenerate parabolic equation
by: Hryntsiv, N. M., et al.
Published: (2011)

Existence and uniqueness of the weak solution of a system of equations of the pa abolic type with singular right-hand sides
by: S. I. Liashko, et al.
Published: (2012)

On boundedness of solutions of Hill&#039;s equation with potential-distribution
by: V. N. Moliboga
Published: (2014)

Boundedness of solutions of differential equations with delayed argument, «close» to the linear
by: Barkovskaya, N. V., et al.
Published: (1966)

On the Dirichlet problem for a quasilinear elliptic second order equation with triple degeneracy and singularity in a domain with edge on the boundary
by: Borsuk, M., et al.
Published: (2000)

Information complexity of weakly singular integral equations
by: Makhkamov, K. Sh., et al.
Published: (1994)

Cauchy problem for non-uniformly parabolic equations with power singularities
by: I. D. Pukalskyi
Published: (2021)

Singularities of Solutions of Singular Integral Equations
by: Il'man, V. M., et al.
Published: (2002)

Boundedness of multilinear singular integral operators on the homogeneous Morrey–Herz spaces
by: Wu, Jianglong, et al.
Published: (2009)

One-Sided Nonlocal Boundary-Value Problem for Singular Parabolic Equations
by: Pukalskyi, I. D., et al.
Published: (2001)

Regularity of a boundary point for singular parabolic equations with measurable coefficients
by: Skrypnik, I. I., et al.
Published: (2004)

On a generalization of a Cauchy problem for singular parabolic type evolution equations
by: V. V. Horodetskyi, et al.
Published: (2016)

Method of energy estimates for the study of a behavior of weak solutions of the equation of slow diffusion with singular boundary data
by: Ye. O. Yevhenieva, et al.
Published: (2019)

Continuability and boundedness of solutions for a kind of nonlinear delay integro-differential equations of third order
by: C. Tunз, et al.
Published: (2017)

Continuability and boundedness of solutions for a kind of nonlinear delay integro-differential equations of third order
by: Tunç, C., et al.
Published: (2017)

Approximate optimal controller for a weakly nonlinear evolutionary equation of parabolic type
by: N. V. Horban, et al.
Published: (2021)

Existence of three weak solutions for fourth-order elastic beam equations on the whole space
by: M. R.H. Tavani
Published: (2020)

Existence of three weak solutions for fourth-order elastic beam equations on the whole space
by: Tavani , M. R. H., et al.
Published: (2020)

Fuchsian Equations with Three Non-Apparent Singularities
by: Eremenko, A., et al.
Published: (2018)

Linear boundary-value problems for weakly singular integral equations
by: O. A. Boichuk, et al.
Published: (2019)

Removability of an isolated singularity of solutions of the Neumann problem for quasilinear parabolic equations with absorption that admit double degeneration
by: Boldovskaya, O. M., et al.
Published: (2010)

On asymptotically stability, uniformly stability and boundedness of solutions of nonlinear Volterra integro-differential equations
by: C. Tunз, et al.
Published: (2020)

On asymptotically stability, uniformly stability and boundedness of solutions of nonlinear Volterra integro-differential equations
by: Tunç, C., et al.
Published: (2020)

On problems without initial conditions for singular parabolic systems
by: M. I. Konarovska
Published: (2012)

Control of singular distributed parabolic systems with discontinuous nonlinearities
by: Pavlenko, V. N., et al.
Published: (1994)

Upper and Lower Bounds of a Solution of the Cauchy Problem for a Stochastic Differential Equation of Parabolic Type with Power Nonlinearities (Weak Source)
by: Mel'nik, S. A., et al.
Published: (2002)

Singularly perturbed multidimensional parabolic equation with rapidly oscillating free term
by: A. S. Omuraliiev, et al.
Published: (2021)