Well‐Posedness Analysis and Numerics of Boundary‐Domain Integral Equation Systems Equivalent to the Robin Problem for the Helmholtz Equation With Variable Coefficients in Lipschitz Domains
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DOI: 10.1002/mma.10965
Abstract: Given the interior Robin boundary value problem (BVP) for the Helmholtz equation with variable coefficients, we use an appropriate parametrix to derive two boundary‐domain integral equation systems (BDIES) equivalent to the original Robin BVP in… read more here.
Keywords: equation; equation variable; variable coefficients; boundary domain ... See more keywords
Stabilization of a one-dimensional wave equation with variable coefficient under non-collocated control and delayed observation
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DOI: 10.1002/mma.4654
Abstract: In this paper, we consider stabilization of a 1-dimensional wave equation with variable coefficient where non-collocated boundary observation suffers from an arbitrary time delay. Since input and output are non-collocated with each other, it is… read more here.
Keywords: equation variable; observation; non collocated; equation ... See more keywords
General Decay for a Viscoelastic Equation of Variable Coefficients in the Presence of Past History with Delay Term in the Boundary Feedback and Acoustic Boundary Conditions
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DOI: 10.1007/s10440-017-0137-y
Abstract: In this paper, we consider a viscoelastic equation of variable coefficients in the presence of infinite memory (past history) with nonlinear damping term and nonlinear delay term in the boundary feedback and acoustic boundary conditions.… read more here.
Keywords: equation variable; term; variable coefficients; history ... See more keywords
Global existence and stability results for a time-fractional diffusion equation with variable exponents
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DOI: 10.1007/s40065-024-00463-2
Abstract: This paper aims to study the existence and stability results concerning a fractional partial differential equation with variable exponent source functions. The local existence result for α∈(0,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}… read more here.
Keywords: existence stability; equation variable; stability results; stability ... See more keywords
Abundant exact solutions for the (3+1)-dimensional generalized nonlinear Schrödinger equation with variable coefficients
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DOI: 10.1016/j.cjph.2020.03.010
Abstract: Abstract The (3+1)-dimensional generalized nonlinear Schrodinger equation with variable coefficients (3D-VcgNLSE) and optical lattice is investigated. Bright and dark soliton solutions are presented by two direct ansatz. Two similar solutions are obtained in terms of… read more here.
Keywords: equation variable; variable coefficients; abundant exact; dimensional generalized ... See more keywords
Nonautonomous solitons for an extended forced Korteweg-de Vries equation with variable coefficients in the fluid or plasma
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DOI: 10.1080/17455030.2017.1356944
Abstract: Abstract Under investigation in this paper is an extended forced Korteweg-de Vries equation with variable coefficients in the fluid or plasma. Lax pair, bilinear forms, and bilinear Bäcklund transformations are derived. Based on the bilinear… read more here.
Keywords: equation variable; variable coefficients; extended forced; vries equation ... See more keywords
Numerical strategy for solving the Boltzmann equation with variable E/N using physics-informed neural networks
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DOI: 10.1088/1361-6463/accbcf
Abstract: A novel strategy to solve the Boltzmann equation with variable reduced electric field E/N by using an artificial neural network (ANN) is introduced, where E is the electric field and N is the gas number… read more here.
Keywords: physics; boltzmann equation; ann; equation variable ... See more keywords
On the Nonlinear Schrödinger Equation with a Variable Damping Term
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DOI: 10.1134/s1995080218090378
Abstract: We consider the L2-critical nonlinear Schrödinger equation with an inhomogeneous damping coefficient a(x). We prove the global existence of the solution in H1(Rd) and we give the minimal time of the blow up for some… read more here.
Keywords: equation variable; dinger equation; nonlinear schr; schr dinger ... See more keywords
Existence, decay and blow-up results for a plate viscoelastic equation with variable-exponent logarithmic terms
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DOI: 10.2298/fil2420051s
Abstract: In the present study, we investigate the solution behavior for a class of fourth-order viscoelastic equation with variable-exponent logarithmic nonlinearities. First, we prove the global existence of solutions, and next, by constructing suitable auxiliary functionals,… read more here.
Keywords: equation variable; existence; variable exponent; viscoelastic equation ... See more keywords
The Time–Fractional Wave Equation with Variable Coefficients
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DOI: 10.3390/math13152369
Abstract: In this paper, we primarily use the inverse operator method to find a unique series solution to a time–fractional wave equation with variable coefficients based on the Mittag–Leffler function. In addition, we also derive the… read more here.
Keywords: equation; equation variable; fractional wave; wave equation ... See more keywords