Recovery of the support of a source term in an elliptic differential equation

1997 ◽  
Vol 13 (4) ◽  
pp. 959-976 ◽  
Author(s):  
Frank Hettlich ◽  
William Rundell
Keyword(s):  
Differential Equation ◽  
Source Term ◽  
Elliptic Differential Equation

scholarly journals Higher Integrability of Weak Solutions to a Class of Double Obstacle Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhenhua Hu ◽  
Shuqing Zhou
Keyword(s):  
Differential Equation ◽  
Weak Solutions ◽  
Second Order ◽  
Obstacle Problems ◽  
Elliptic Differential Equation ◽  
Higher Integrability ◽  
Global Higher Integrability ◽  
Quasilinear Elliptic

We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equationdiv(A(x,∇u))=div f(x,u), whereA(x,∇u),f(x,u)are twon×Nmatrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems.

scholarly journals On a Differential Equation Involving Hilfer-Hadamard Fractional Derivative

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
M. D. Qassim ◽  
K. M. Furati ◽  
N.-E. Tatar
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Global Solution ◽  
Differential Inequality ◽  
Source Term ◽  
Existence Of Solutions ◽  
Hadamard Fractional Derivative ◽  
Fractional Differential

This paper studies a fractional differential inequality involving a new fractional derivative (Hilfer-Hadamard type) with a polynomial source term. We obtain an exponent for which there does not exist any global solution for the problem. We also provide an example to show the existence of solutions in a wider space for some exponents.

scholarly journals Existence of Bounded Solutions to a Modified Version of the Bagley–Torvik Equation

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 289
Author(s):  
Daniel Cao Labora ◽  
José António Tenreiro Machado
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Thin Plate ◽  
Newtonian Fluid ◽  
Physical Meaning ◽  
Source Term ◽  
Vertical Motion ◽  
Bounded Solutions ◽  
Clear Physical Meaning ◽  
Fractional Differential

This manuscript reanalyses the Bagley–Torvik equation (BTE). The Riemann–Liouville fractional differential equation (FDE), formulated by R. L. Bagley and P. J. Torvik in 1984, models the vertical motion of a thin plate immersed in a Newtonian fluid, which is held by a spring. From this model, we can derive an FDE for the particular case of lacking the spring. Here, we find conditions for the source term ensuring that the solutions to the equation of the motion are bounded, which has a clear physical meaning.

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