scholarly journals A Gevrey class semigroup for a thermoelastic plate model with a fractional Laplacian: Between the Euler-Bernoulli and Kirchhoff models

2020 ◽  
Vol 40 (5) ◽  
pp. 2875-2889
Author(s):  
Valentin Keyantuo ◽  
◽  
Louis Tebou ◽  
Mahamadi Warma ◽  
◽  
...  
Keyword(s):  
Fractional Laplacian ◽  
Gevrey Class ◽  
Plate Model ◽  
Thermoelastic Plate

scholarly journals Null controllability of a thermoelastic plate

2002 ◽  
Vol 7 (11) ◽  
pp. 585-599 ◽  
Author(s):  
Assia Benabdallah ◽  
Maria Grazia Naso
Keyword(s):  
Thermal Control ◽  
Finite Energy ◽  
Null Controllability ◽  
Energy Solution ◽  
Plate Model ◽  
Time And Space ◽  
Thermal Equation ◽  
Control Time ◽  
Thermoelastic Plate ◽  
Finite Energy Solution

Thermoelastic plate model with a control term in the thermal equation is considered. The main result in this paper is that with thermal control, locally distributed within the interior and square integrable in time and space, any finite energy solution can be driven to zero at the control timeT.

scholarly journals Local versus nonlocal elliptic equations: short-long range field interactions

2020 ◽  
Vol 10 (1) ◽  
pp. 895-921
Author(s):  
Daniele Cassani ◽  
Luca Vilasi ◽  
Youjun Wang
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Principle ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Spectral Properties ◽  
Fractional Laplacian ◽  
Coupling Parameter ◽  
Nonlocal Operators ◽  
The Maximum Principle ◽  
Regularity Results

Abstract In this paper we study a class of one-parameter family of elliptic equations which combines local and nonlocal operators, namely the Laplacian and the fractional Laplacian. We analyze spectral properties, establish the validity of the maximum principle, prove existence, nonexistence, symmetry and regularity results for weak solutions. The asymptotic behavior of weak solutions as the coupling parameter vanishes (which turns the problem into a purely nonlocal one) or goes to infinity (reducing the problem to the classical semilinear Laplace equation) is also investigated.

scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

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