Asymptotic output tracking for a class of semilinear parabolic equations: A semianalytical approach
Sign Up to like & getrecommendations! Published in 2019 at "International Journal of Robust and Nonlinear Control"
DOI: 10.1002/rnc.4504
Abstract: This paper addresses the problem of asymptotic output tracking of a class of semilinear parabolic equations with pointwise in‐domain actuation. First, the assessment of the well‐posedness of the considered systems is performed, and then, the… read more here.
Keywords: parabolic equations; tracking class; class semilinear; output tracking ... See more keywords
A Priori Error Estimates for State-Constrained Semilinear Parabolic Optimal Control Problems
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Optimization Theory and Applications"
DOI: 10.1007/s10957-018-1311-8
Abstract: We consider the finite element discretization of semilinear parabolic optimization problems subject to pointwise in time constraints on mean values of the state variable. In order to control the feasibility violation induced by the discretization,… read more here.
Keywords: semilinear parabolic; state; control; optimization ... See more keywords
Asymptotic Behavior of Solutions to Semilinear Parabolic Equations with Infinite Delay
Sign Up to like & getrecommendations! Published in 2018 at "Acta Mathematica Vietnamica"
DOI: 10.1007/s40306-018-0289-5
Abstract: We consider a class of semilinear parabolic equations with infinite delay and nonlinearity of polynomial type. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we show the… read more here.
Keywords: semilinear parabolic; asymptotic behavior; infinite delay; parabolic equations ... See more keywords
Time-dependent singularities in semilinear parabolic equations: Existence of solutions
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2017.07.016
Abstract: Abstract We study the existence of solutions of the semilinear parabolic equation ∂ t u − Δ u = u p + Λ in D ′ ( R N × I ) . Here N… read more here.
Keywords: semilinear parabolic; time dependent; singularities semilinear; parabolic equations ... See more keywords
Superconvergence analysis for a semilinear parabolic equation with BDF-3 finite element method
Sign Up to like & getrecommendations! Published in 2020 at "Applicable Analysis"
DOI: 10.1080/00036811.2020.1789594
Abstract: The main aim of this paper is to obtain superconvergence result for a semilinear parabolic equation with 3-step backward differential formula Galerkin finite element method. The time-discrete syste... read more here.
Keywords: semilinear parabolic; finite element; element method; parabolic equation ... See more keywords
Robust Control for Semilinear Parabolic Distributed Parameter Systems With External Disturbances via Mobile Actuators and Sensors.
Sign Up to like & getrecommendations! Published in 2022 at "IEEE transactions on cybernetics"
DOI: 10.1109/tcyb.2022.3150171
Abstract: This article presents a robust feedback compensator design approach for semilinear parabolic distributed parameter systems (DPSs) with external disturbances via mobile actuators and sensors. An performance constraint is introduced to deal with the external disturbances… read more here.
Keywords: mobile actuators; external disturbances; actuators sensors; parabolic distributed ... See more keywords
Fuzzy Stabilization Design for Semilinear Parabolic PDE Systems With Mobile Actuators and Sensors
Sign Up to like & getrecommendations! Published in 2020 at "IEEE Transactions on Fuzzy Systems"
DOI: 10.1109/tfuzz.2019.2908139
Abstract: This paper deals with a fuzzy stabilization design problem for a class of semilinear parabolic partial differential equation (PDE) systems using mobile actuators and sensors. Initially, a Takagi–Sugeno (T–S) fuzzy PDE model is employed to… read more here.
Keywords: pde; actuator sensor; stabilization; semilinear parabolic ... See more keywords
First Boundary Value Problem for Cordes-Type Semilinear Parabolic Equation with Discontinuous Coefficients
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DOI: 10.1155/2020/1019038
Abstract: For a class of semilinear parabolic equations with discontinuous coefficients, the strong solvability of the Dirichlet problem is studied in this paper. 'e problem ????ni,j�1 aij(t, x)uxixj − ut + g(t, x, u) � f(t,… read more here.
Keywords: semilinear parabolic; discontinuous coefficients; first boundary; value problem ... See more keywords
A Finite Element Domain Decomposition Approximation for a Semilinear Parabolic Singularly Perturbed Differential Equation
Sign Up to like & getrecommendations! Published in 2017 at "International Journal of Nonlinear Sciences and Numerical Simulation"
DOI: 10.1515/ijnsns-2015-0156
Abstract: Abstract In this paper, we propose a Monotone Schwarz Iterative Method (MSIM) under the framework of Domain Decomposition Strategy for solving semilinear parabolic singularly perturbed partial differential equations (SPPDEs). A three-step Taylor Galerkin Finite Element… read more here.
Keywords: semilinear parabolic; singularly perturbed; parabolic singularly; domain decomposition ... See more keywords
Optimal singularities of initial functions for solvability of a semilinear parabolic system
Sign Up to like & getrecommendations! Published in 2021 at "Journal of the Mathematical Society of Japan"
DOI: 10.2969/jmsj/86058605
Abstract: Let $(u,v)$ be a nonnegative solution to the semilinear parabolic system \[ \mbox{(P)} \qquad \cases{ \partial_t u=D_1\Delta u+v^p, & $x\in{\bf R}^N,\,\,\,t>0,$\\ \partial_t v=D_2\Delta v+u^q, & $x\in{\bf R}^N,\,\,\,t>0,$\\ (u(\cdot,0),v(\cdot,0))=(\mu,\nu), & $x\in{\bf R}^N,$ } \] where $D_1$,… read more here.
Keywords: semilinear parabolic; initial functions; parabolic system; optimal singularities ... See more keywords