scholarly journals Existence and uniqueness of weak solutions to the singular kernels coagulation equation with collisional breakage

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Prasanta Kumar Barik ◽  
Ankik Kumar Giri
Keyword(s):  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Singular Kernels ◽  
Coagulation Equation

EXISTENCE AND UNIQUENESS OF WEAK AND CLASSICAL SOLUTIONS FOR A FOURTH-ORDER SEMILINEAR BOUNDARY VALUE PROBLEM

2019 ◽  
Vol 61 (3) ◽  
pp. 305-319
Author(s):  
CRISTIAN-PAUL DANET
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Fourth Order ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Classical Solutions ◽  
Maximum Principles ◽  
Uniqueness Results

This paper is concerned with the problem of existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem. The existence and uniqueness for weak solutions follows from standard variational methods, while similar uniqueness results for classical solutions are derived using maximum principles.

Regularity of weak solutions for the relativistic Vlasov–Maxwell system

2018 ◽  
Vol 15 (04) ◽  
pp. 693-719 ◽  
Author(s):  
Nicolas Besse ◽  
Philippe Bechouche
Keyword(s):  
Electromagnetic Field ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Regularity Of Solutions ◽  
Maxwell System ◽  
Smoothing Effect ◽  
Regular Solutions ◽  
Low Velocity ◽  
Regularity Of Weak Solutions ◽  
The One

We investigate the regularity of weak solutions of the relativistic Vlasov–Maxwell system by using Fourier analysis and the smoothing effect of low velocity particles. This smoothing effect has been used by several authors (see Glassey and Strauss 1986; Klainerman and Staffilani, 2002) for proving existence and uniqueness of [Formula: see text]-regular solutions of the Vlasov–Maxwell system. This smoothing mechanism has also been used to study the regularity of solutions for a kinetic transport equation coupled with a wave equation (see Bouchut, Golse and Pallard 2004). Under the same assumptions as in the paper “Nonresonant smoothing for coupled wave[Formula: see text]+[Formula: see text]transport equations and the Vlasov–Maxwell system”, Rev. Mat. Iberoamericana 20 (2004) 865–892, by Bouchut, Golse and Pallard, we prove a slightly better regularity for the electromagnetic field than the one showed in the latter paper. Namely, we prove that the electromagnetic field belongs to [Formula: see text], with [Formula: see text].

scholarly journals Kawahara-Burgers Equation on a Strip

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
N. A. Larkin
Keyword(s):  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Burgers Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Regular Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Initial Boundary Value ◽  
Channel Type

An initial-boundary value problem for the 2D Kawahara-Burgers equation posed on a channel-type strip was considered. The existence and uniqueness results for regular and weak solutions in weighted spaces as well as exponential decay of small solutions without restrictions on the width of a strip were proven both for regular solutions in an elevated norm and for weak solutions in theL2-norm.

Unique Strong Solutions and V -Attractors of a Three Dimensional System of Globally Modified Navier-Stokes Equations

2006 ◽  
Vol 6 (3) ◽  
Author(s):  
Tomás Caraballo ◽  
José Real ◽  
Peter E. Kloeden
Keyword(s):  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Dimensional System ◽  
Navier Stokes Equations ◽  
Three Dimensional System

AbstractWe prove the existence and uniqueness of strong solutions of a three dimensional system of globally modified Navier-Stokes equations. The flattening property is used to establish the existence of global V -attractors and a limiting argument is then used to obtain the existence of bounded entire weak solutions of the three dimensional Navier-Stokes equations with time independent forcing.

scholarly journals Remarks on weak solutions for a nonlocal parabolic problem

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
S. B. de Menezes
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Parabolic Problem ◽  
Galerkin Approximation ◽  
Diffusion Problem ◽  
Fixed Point Result ◽  
Nonlinear Diffusions

We prove a result on existence and uniqueness of weak solutions for a diffusion problem associated with nonlinear diffusions of nonlocal type studied by Chipot and Lovat (1999) by an application of the fixed point result of Schauder. Moreover, making use of Faedo-Galerkin approximation, coupled with some technical ideas, we establish a result on existence of periodic solution.

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