scholarly journals Existence and uniqueness of maximal strong solution of a 1D blood flow in a network of vessels

2022 ◽  
Vol 63 ◽  
pp. 103405
Author(s):  
Debayan Maity ◽  
Jean-Pierre Raymond ◽  
Arnab Roy
Keyword(s):  
Blood Flow ◽  
Strong Solution ◽  
Existence And Uniqueness

scholarly journals Analysis of a non-linear model of populations structured by size

2020 ◽  
Vol 101 (3) ◽  
pp. 734-750
Author(s):  
Anna Lo Grasso ◽  
Silvia Totaro
Keyword(s):  
Linear Model ◽  
Strong Solution ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Marine Invertebrates ◽  
Life Stage ◽  
Pelagic Larvae ◽  
Non Linear ◽  
Local Habitat

AbstractThe model we study deals with a population of marine invertebrates structured by size whose life stage is composed of adults and pelagic larvae such as barnacles contained in a local habitat. We prove existence and uniqueness of a continuous positive global mild solution and we give an estimate of it. We prove also that this solution is the strong solution of the problem.

scholarly journals On a class of singular hyperbolic equation with a weighted integral condition

1999 ◽  
Vol 22 (3) ◽  
pp. 511-519 ◽  
Author(s):  
Said Mesloub ◽  
Abdelfatah Bouziani
Keyword(s):  
Hyperbolic Equation ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
Nonlocal Condition ◽  
A Priori ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Priori Estimate ◽  
Weighted Integral

In this paper, we study a mixed problem with a nonlocal condition for a class of second order singular hyperbolic equations. We prove the existence and uniqueness of a strong solution. The proof is based on a priori estimate and on the density of the range of the operator generated by the studied problem.

scholarly journals Boundary value problem with integral conditions for a linear third-order equation

2003 ◽  
Vol 2003 (11) ◽  
pp. 553-567 ◽  
Author(s):  
M. Denche ◽  
A. Memou
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Order Equation ◽  
Integral Conditions ◽  
Third Order ◽  
Integral Boundary

We prove the existence and uniqueness of a strong solution for a linear third-order equation with integral boundary conditions. The proof uses energy inequalities and the density of the range of the generated operator.

scholarly journals INFINITELY MANY BROWNIAN GLOBULES WITH BROWNIAN RADII

2010 ◽  
Vol 10 (04) ◽  
pp. 591-612
Author(s):  
MYRIAM FRADON ◽  
SYLVIE RŒLLY
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Strong Solution ◽  
Local Time ◽  
Existence And Uniqueness ◽  
Infinite System ◽  
Time Dependent ◽  
Initial Condition ◽  
Infinite Dimensional ◽  
Time Existence

We consider an infinite system of non-overlapping globules undergoing Brownian motions in ℝ3. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is modelized by an infinite-dimensional stochastic differential equation with local time. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also find a class of reversible measures.

A THEOREM DUAL TO YAMADA–WATANABE THEOREM FOR STOCHASTIC EVOLUTION EQUATIONS

2010 ◽  
Vol 10 (03) ◽  
pp. 367-374 ◽  
Author(s):  
HUIJIE QIAO
Keyword(s):  
Evolution Equation ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Variational Approach ◽  
Evolution Equations ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Uniqueness In Law ◽  
Strong Existence

In this paper, we prove that uniqueness in law and strong existence for a stochastic evolution equation [Formula: see text] imply existence and uniqueness of a strong solution in the framework of the variational approach. This result seems to be dual to Yamada–Watanabe theorem in [7].

REGULARITY OF SOLUTIONS TO LINEAR STOCHASTIC SCHRÖDINGER EQUATIONS

2007 ◽  
Vol 10 (02) ◽  
pp. 237-259 ◽  
Author(s):  
CARLOS M. MORA ◽  
ROLANDO REBOLLEDO
Keyword(s):  
Strong Solution ◽  
Existence And Uniqueness ◽  
Mean Value ◽  
Quantum Measurements ◽  
Regularity Of Solutions ◽  
Schrodinger Equations ◽  
Quantum Trajectories ◽  
Initial Condition ◽  
Schrödinger Equations ◽  
The Mean

We develop linear stochastic Schrödinger equations driven by standard cylindrical Brownian motions (LSSs) that unravel quantum master equations in Lindblad form into quantum trajectories. More precisely, this paper establishes the existence and uniqueness of the smooth strong solution Xt to a LSS with regular initial condition. Moreover, we obtain that the mean value of the square norm of Xt is constant. We also treat the approximation of LSSs by ordinary stochastic differential equations. We apply our results to: (i) models of quantum measurements of position and momentum; and (ii) a system formed by fermions.

A Strong Solution of an Evolution Problem with Integral Conditions

2002 ◽  
Vol 9 (1) ◽  
pp. 149-159
Author(s):  
S. Mesloub ◽  
A. Bouziani ◽  
N. Kechkar
Keyword(s):  
Functional Analysis ◽  
Parabolic Equation ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Energy Inequality ◽  
Integral Boundary Conditions ◽  
Analysis Method ◽  
Integral Conditions ◽  
Integral Boundary ◽  
Singular Parabolic Equation

Abstract The paper is devoted to proving the existence and uniqueness of a strong solution of a mixed problem with integral boundary conditions for a certain singular parabolic equation. A functional analysis method is used. The proof is based on an energy inequality and on the density of the range of the operator generated by the studied problem.

scholarly journals Global Weak Solutions for the Weakly Dissipative Dullin-Gottwald-Holm Equation

2021 ◽  
pp. 91-108
Author(s):  
Shiyu Li
Keyword(s):  
Initial Data ◽  
Surface Waves ◽  
Shallow Water ◽  
Strong Solution ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Water Regime ◽  
Global Weak Solutions ◽  
Holm Equation ◽  
Sign Conditions

In this paper, we are concerned with the existence and uniqueness of global weak solutions for the weakly dissipative Dullin-Gottwald-Holm equation describing the unidirectional propagation of surface waves in shallow water regime:                                        ut − α2uxxt + c0ux + 3uux + γuxxx + λ(u − α2uxx) = α2(2uxuxx + uuxxx).Our main conclusion is that on c0 = − γ/α2 and λ ≥ 0, if the initial data satisfies certain sign conditions, then we show that the equation has corresponding strong solution which exists globally in time, finally we demonstrate the existence and uniqueness of global weak solutions to the equation.

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