What is the application of the partial differential equations with Hardy potential?

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How to prove that \int_\Omega u dx is the smallest value when \Omega is a unit ball?

For connected C^2 domain \Omega such that |\Omega|=|B_1(0)|, let u be the soluiton of -\Delta u=1 in \Omega, u=0 on \partial \Omega, when the value \int_\Omega u dx takes the minimum? is it the...

04 May 2017 3,799 3 View

How to explain the temperature of the earth?

The earth has formed so many years. The inner temperature are much higher than the surface and it it keep balanced. It seems dificult to explain this by the Heat equation. Does some one know why...

07 August 2016 1,843 0 View

Does some one know how to build fast decaying solutions for fractional semilinear equations?

I want to know how to build the fast decaying solution for (-\Delta)^\alpha u=u^p in R^N\setminus {0} where p>\frac{N}{N-2\alpha}. Here fast decay means the solution hjas decaying rate...

11 December 2015 3,054 6 View

Does anyone know if the method of moving planes could be used to obtain radial symmetry of the solution of ellitptic equation with gradient?

To prove the radial symmetry, the method of moving plane is a very useful tool. But how to do the moving planes for equations like -\Delta u =|\nable u|^p in B_1, u=0 on \partial B_1(0).

05 June 2015 5,444 1 View

Does anyone know the estimate of Green's function of the regional fractional laplacain?

The regional fractional laplacian is defined by (-\Delta)_D^a u(x)=-C P:V. \int_D\frac{u(y)-u(z)}{|y-z|^{N+2a}}dy, where D is a C^2 domain.

10 November 2014 1,624 5 View

How to prove the x_N-odd solution of -\Delta u+|u|^pu=f in B_1, where f is x_N-odd?

We know that the solution of -\Delta u=f in B_1 is x_N-odd when f is x_N odd.

07 August 2014 2,866 3 View

Does anybody know if one could characterize the boundary blow-up solution to PDE in the measure framework?

Boundary blow-up solution is usually found by Perron's method in the classical sense.

02 March 2014 1,222 2 View

How can I prepare virus for a TEM or SEM imaging?

I have virus (viral hemorrhagic septicemia virus) in suspension and the experiment will not involve cells. What level of TCID50 is preferred?

11 August 2024 3,115 1 View

Handling Missing Data and Building a Predictive Model with Incomplete Information ?

I am developing a predictive model for a water supply network that involves 20 influencing points. However, I only have historical data for 10 out of these 20 points. I would like to know how to...

10 August 2024 4,005 2 View

Is it possible to use the Fused Deposition Modeling (FDM) to additively manufacture interconnected porous structure generation of >100-200 micrometer?

Usually, additive manufacturing techniques like SEBM, SLS, and SLM are used for interconnected porous lattice structure generation with sizes of >100–200 micrometers. Can the Fused Deposition...

09 August 2024 7,892 0 View

How to define an anisotropic material with asymmetric elastic compliance/stiffness matrix in ANSYS APDL?

I need to model an anisotropic material in which the Poisson's ratio ν_12 ≠ ν_21 and so on. Therefore, the elastic compliance matrix wouldn't be a symmetric one. In ANSYS APDL, for TB,ANEL...

09 August 2024 5,048 2 View

How can I apply boundary conditions in an orthotropic steel deck numerical model using ABAQUS software?

I am trying to simulate vehicular loading on an orthotopic steel deck bridge section in ABAQUS software. The red arrow mark in the attached figure indicates the direction in which the vehicle will...

08 August 2024 719 0 View

Can you suggest reliable sources defining "3D mesh" and "3D city models"?

Dear fellow researchers, I am currently working on a paper where I need to provide a reliable reference that defines and distinguishes between 3D mesh models and 3D city models. Although I am...

06 August 2024 9,986 2 View

Please explain how the plastic input value should be considered from the true stress-strain curve for the bilinear elastoplastic material model ?

I am working on Abaqus/Explicit(Quasistatic ) for the deformation of the auxetic structure model. Please explain how the plastic input value should be considered from the true stress-strain curve...

05 August 2024 454 3 View

What are the shear and normal stiffness values of an LLDPE liner in 3D numerical modeling of a stockpile?

I am seeking experimental or applicable data for the liner (LLDPE) interface in FLAC3D numerical modeling of a large stockpile. Could you please recommend suitable references? The preferred data...

05 August 2024 3,665 0 View

Request a single Lecture notes for math as detailed as this that I can find in one place?

- The Existence/Uniqueness of Solutions to Higher Order Linear Differential Equations - Higher Order Homogenous Differential Equations - Wronskian Determinants of $n$ Functions - Wronskian...

03 August 2024 2,366 0 View

Is it necessary to covary exogenous constructs in a structural model?

I am working on a SEM model where i have 7 latent variables (6 exogenous and 1 endogenous). In AMOS when I co-vary the exogenous constructs, only 2 paths are coming significant out of 6. But when...

03 August 2024 6,028 4 View