1,721,100 research outputs found
Controllability for the Burgers model
No full textIn this paper we study vibrations of viscoelastic materials, whose behaviour can be represented by mechanical models given as combinations of springs and dashpots, and establish reachability results.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/)
A Semilinear Integro-Differential Equation: Global Existence and Hidden Regularity
No full textHere we show a hidden regularity result for nonlinear wave equations with an integral term of convolution type and Dirichlet boundary conditions. Under general assumptions on the nonlinear term and on the integral kernel we are able to state results about global existence of strong and mild solutions without any further smallness on the initial data. Then we define the trace of the normal derivative of the solution showing a regularity result. In such a way we extend to integrodifferential equations with nonlinear term well-known results available in the literature for linear wave equations with memory
Foundation of the time-fractional beam equation
No full textWe derive the model for fractional beam equations by making use of a modified constitutive assumption, that is the relationship between stress and strain depending on the creep compliance given by a fractional power-type function
Trace regularity for biharmonic evolution equations with Caputo derivatives
No full textOur goal is to establish a hidden regularity result for solutions of time fractional Petrovsky systems. The order α of the Caputo fractional derivative belongs to the interval (1, 2). We achieve such result for a suitable class of weak solutions
Fractional diffusion-wave equations: hidden regularity for weak solutions
No full textWe prove a "hidden"regularity result for weak solutions of time fractional diffusion-wave equations where the Caputo fractional derivative is of order α ε (1, 2). To establish such result we analyse the regularity properties of the weak solutions in suitable interpolation spaces
Weak solutions for time-fractional evolution equations in hilbert spaces
No full textOur purpose is to introduce a notion of weak solution for a class of abstract fractional differential equations. We point out that the time fractional derivative occurring in the equations is in the sense of the Caputo derivative. We prove existence results for weak and strong solutions. To justify the abstract theory we develop, we apply two examples of concrete equations: time-fractional wave equations and time-fractional Petrovsky systems. Both these concrete examples are of great interest in the theory of fractional partial differential equations
An object-oriented approach to idempotent analysis: Integral equations as optimal control problems
No full textDesign and evaluation of a scalable engine for 3D-FFT computation in an FPGA cluster
No full textThe Three Dimensional Fast Fourier Transform (3D-FFT) is commonly used to solve the partial differential equations describing the system evolution in several physical phenomena, such as the motion of viscous fluids described by the Navier-Stokes equations. Simulation of such problems requires the use of a parallel High-Performance Computing architecture since the size of the problem grows with the cube of the FFT size, and the representation of the single point comprises several double precision floatingpoint complex numbers. Modern High-Performance Computing (HPC) systems are considering the inclusion of FPGAs as components of this computing architecture because they can combine effective hardware acceleration capabilities and dedicated communication facilities. Furthermore, the network topology can be optimized for the specific calculation that the cluster must perform, especially in the case of algorithms limited by the data exchange delay between the processors. In this paper, we explore an HPC design that uses FPGA accelerators to compute the 3DFFT. We devise a scalable FFT engine based on a custom radix-2 double precision core that is used to implement the Decimation in Frequency version of the Cooley-Tukey FFT algorithm. The FFT engine can be adapted to different technology constraints and networking topologies by adjusting the number of cores and configuration parameters in order to minimize the overall calculation time. We compare the various possible configurations with the technological limits of available hardware. Finally, we evaluate the bandwidth required for continuous FFT execution in the APEnet toroidal mesh network
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