Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Linear Differential Equations01:27

Linear Differential Equations

118
The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law...
118
Separable Differential Equations01:20

Separable Differential Equations

133
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
133
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

1.0K
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
1.0K
Second Uniqueness Theorem01:16

Second Uniqueness Theorem

2.7K
Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
2.7K
Continuity Equation01:28

Continuity Equation

3.4K
The continuity equation asserts that the mass flow rate must remain constant for a steady flow of an incompressible fluid within a confined system. This principle applies to systems where fluid passes through varying cross-sectional areas, such as nozzles, syringes, and pipes.
The mass flow rate is expressed as:
3.4K
Continuity Equation01:20

Continuity Equation

1.6K
The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area can be written as the surface integral of the current density.
1.6K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Quantitative unique continuation for the heat equations with inverse square potential.

Journal of inequalities and applications·2019
Same author

Enzyme catalysis: tool to make and break amygdalin hydrogelators from renewable resources: a delivery model for hydrophobic drugs.

Journal of the American Chemical Society·2006
Same author

Theoretical probing of deltahedral closo-auroboranes B(x)Au(x)2- (x = 5-12).

Inorganic chemistry·2006
Same author

Density functional theory/time-dependent DFT studies on the structures, trend in DNA-binding affinities, and spectral properties of complexes [Ru(bpy)2(p-R-pip)]2+ (R = -OH, -CH3, -H, -NO2).

The journal of physical chemistry. A·2006
Same author

Sn12(2-): stannaspherene.

Journal of the American Chemical Society·2006
Same author

High efficient mammalian expression and secretion of a functional humanized single-chain Fv/human interleukin-2 molecules.

World journal of gastroenterology·2006
Same journal

The infimum values of two probability functions for the Gamma distribution.

Journal of inequalities and applications·2024
Same journal

The existence of nonnegative solutions for a nonlinear fractional <i>q</i>-differential problem via a different numerical approach.

Journal of inequalities and applications·2021
Same journal

Correction to: On the spectral norms of <i>r</i>-circulant matrices with the bi-periodic Fibonacci and Lucas numbers.

Journal of inequalities and applications·2019
Same journal

Erratum to: General Bahr-Esseen inequalities and their applications.

Journal of inequalities and applications·2019
Same journal

Hermite-Hadamard type inequalities for <i>F</i>-convex function involving fractional integrals.

Journal of inequalities and applications·2019
Same journal

Global maximal inequality to a class of oscillatory integrals.

Journal of inequalities and applications·2019
See all related articles

Related Experiment Video

Updated: Feb 21, 2026

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
10:23

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

1.1K

Quantitative unique continuation for the linear coupled heat equations.

Guojie Zheng1, Keqiang Li1, Jun Li1

  • 1College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007 P.R. China.

Journal of Inequalities and Applications
|October 10, 2017
PubMed
Summary
This summary is machine-generated.

This study establishes unique continuation for coupled heat equations, proving solutions are uniquely determined by partial data. This advances understanding of heat equation analysis and inverse problems.

Keywords:
coupled heat equationsfrequency functionsunique continuation

More Related Videos

Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
04:35

Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment

Published on: July 5, 2024

2.4K
The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

9.1K

Related Experiment Videos

Last Updated: Feb 21, 2026

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
10:23

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

1.1K
Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
04:35

Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment

Published on: July 5, 2024

2.4K
The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

9.1K

Area of Science:

  • Partial Differential Equations
  • Mathematical Analysis
  • Heat Transfer

Background:

  • Coupled heat equations model complex thermal phenomena.
  • Unique continuation problems are crucial for inverse problems and data assimilation.
  • Previous research often focused on single heat equations or specific domains.

Purpose of the Study:

  • To establish quantitative unique continuation results for coupled heat equations.
  • To demonstrate unique determination of solutions from partial data within a bounded convex domain.
  • To analyze the impact of homogeneous Dirichlet boundary conditions.

Main Methods:

  • Utilizing advanced techniques in partial differential equations.
  • Developing quantitative estimates for unique continuation.
  • Applying functional analysis on a bounded convex domain Ω with a smooth boundary ∂Ω.

Main Results:

  • Established a quantitative unique continuation result for the coupled heat equations.
  • Demonstrated that solution values can be uniquely determined by their values on an arbitrary open subset ω of Ω.
  • Showed this determination is possible at any given positive time T.

Conclusions:

  • The findings provide a strong theoretical foundation for inverse problems involving coupled heat equations.
  • This work contributes to the field of mathematical analysis by extending unique continuation principles.
  • The results have potential implications for வெப்ப பரிமாற்ற (heat transfer) modeling and analysis.