The reconstruction of a parabolic system
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DOI: 10.1002/mma.4440
Abstract: We are concerned with the identification and reconstruction of the coefficients of a linear parabolic system from finite time observations of the solution on the boundary. We present two procedures depending on whether the spectrum… read more here.
Keywords: parabolic system; system; reconstruction parabolic;
Global Existence and Decay Estimates of Solutions of a Parabolic–Elliptic–Parabolic System for Ion Transport Networks
Sign Up to like & getrecommendations! Published in 2020 at "Results in Mathematics"
DOI: 10.1007/s00025-020-1172-y
Abstract: This paper deals with a parabolic-elliptic-parabolic system arising from ion transport networks originally proposed by Albi et al. (Anal Appl 14(1):185–206, 2016). Our investigation demonstrates that the local existence of the weak solution can always… read more here.
Keywords: transport networks; parabolic system; system; parabolic elliptic ... See more keywords
Uniform Attractor for an N-Dimensional Parabolic System with Impulsive Perturbation
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DOI: 10.1007/s10958-021-05299-1
Abstract: We consider a weakly nonlinear N-dimensional parabolic system whose solutions are subjected to impulsive perturbations upon attainment of a certain fixed subset in the phase space. For broad classes of impulsive perturbations, it is proved… read more here.
Keywords: parabolic system; system; dimensional parabolic; uniform attractor ... See more keywords
Sharp pointwise estimates for solutions of weakly coupled second-order parabolic system in a layer
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DOI: 10.1080/17476933.2020.1797707
Abstract: ABSTRACT We deal with m-component vector-valued solutions to the Cauchy problem for a linear both homogeneous and nonhomogeneous weakly coupled second-order parabolic system in the layer . We assume that coefficients of the system are… read more here.
Keywords: order parabolic; coupled second; parabolic system; system ... See more keywords
Carleman Estimate for a Hyperbolic-Parabolic System
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DOI: 10.1134/s001226611902006x
Abstract: A Carleman estimate is obtained for the solutions of a hyperbolic-parabolic system adjoint to the Navier–Stokes equations for a compressible medium. read more here.
Keywords: carleman estimate; hyperbolic parabolic; parabolic system; estimate hyperbolic ... See more keywords
Higher integrability for weak solutions to a degenerate parabolic system with singular coefficients
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DOI: 10.1186/s13661-019-1285-y
Abstract: AbstractIn this paper, we study the degenerate parabolic system uti+Xα∗(aijαβ(z)Xβuj)=gi(z,u,Xu)+Xα∗fiα(z,u,Xu),$$ u_{t}^{i} + X_{\alpha }^{*} \bigl(a_{ij}^{\alpha \beta }(z){X_{\beta }} {u^{j}}\bigr) = {g_{i}}(z,u,Xu) + X_{\alpha }^{*} f_{i}^{\alpha }(z,u,Xu), $$ where X={X1,…,Xm}$X=\{X_{1},\ldots,X_{m} \}$ is a system of smooth… read more here.
Keywords: parabolic system; system; weak solutions; degenerate parabolic ... See more keywords
Optimal singularities of initial functions for solvability of a semilinear parabolic system
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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
Approximate Optimal Control for a Parabolic System with Perturbations in the Coefficients on the Half-Axis
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DOI: 10.3390/axioms11040175
Abstract: In this paper, we use the averaging method to find an approximate solution in the optimal control problem of a parabolic system with non-linearity of the form f(t/ε,y) on an infinite time interval. read more here.
Keywords: control parabolic; optimal control; approximate optimal; parabolic system ... See more keywords
Existence of Positive Solutions and Its Asymptotic Behavior of (p(x), q(x))-Laplacian Parabolic System
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DOI: 10.3390/sym11030332
Abstract: This paper deals with the existence of positively solution and its asymptotic behavior for parabolic system of ( p ( x ) , q ( x ) ) -Laplacian system of partial differential equations using… read more here.
Keywords: asymptotic behavior; existence positive; parabolic system; system ... See more keywords
Analysis of Solutions to a Parabolic System with Absorption
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DOI: 10.3390/sym14061274
Abstract: In this paper, we investigate the blow-up rate and global existence of solutions to a parabolic system with absorption under the homogeneous Dirichlet boundary. By using the comparison principle and super-sub solution method, we obtain… read more here.
Keywords: solutions parabolic; analysis solutions; parabolic system; system absorption ... See more keywords