waveguides,
error estimation,
blow-up,
initial-boundary value problem,
Sobolev type equations.
UDC:
519.63, 519.634, 517.957
Subject:
Waveguide theory
Treatment of equation related to wave propagation (both analytic and numerical). Non-linear functional analysis.
Main publications:
Bogolyubov A. N., Malykh M. D., Panin A. A. Time Asymptotics of a Field Excited in a Waveguide by a Harmonic Current. // Comp. Math. and Math. Physics. Vol. 45, no. 12 (2005).
M. O. Korpusov, A. A. Panin, A. E. Shishkov, “On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type”, Izv. RAN. Ser. Mat., 85:1 (2021), 118–153; Izv. Math., 85:1 (2021), 111–144
A. A. Panin, G. I. Shlyapugin, “Local Solvability and Global Unsolvability of a Model of Ion-Sound Waves in a Plasma”, Mat. Zametki, 107:3 (2020), 426–441; Math. Notes, 107:3 (2020), 464–477
M. O. Korpusov, A. A. Panin, “Instantaneous blow-up versus local solubility of the Cauchy problem for a two-dimensional equation
of a semiconductor with heating”, Izv. RAN. Ser. Mat., 83:6 (2019), 104–132; Izv. Math., 83:6 (2019), 1174–1200
I. I. Kolotov, A. A. Panin, “On Nonextendable Solutions and Blow-Ups of Solutions of Pseudoparabolic Equations with Coercive and Constant-Sign Nonlinearities: Analytical and Numerical Study”, Mat. Zametki, 105:5 (2019), 708–723; Math. Notes, 105:5 (2019), 694–706
V. A. Vasil'chenko, M. O. Korpusov, D. V. Lukyanenko, A. A. Panin, “A study of self-oscillation instability in varicap-based electrical networks: analytical and numerical approaches”, Num. Meth. Prog., 20:3 (2019), 323–336
M. O. Korpusov, D. V. Lukyanenko, A. A. Panin, E. V. Yushkov, “Blow-up of solutions of a full non-linear equation of ion-sound waves
in a plasma with non-coercive non-linearities”, Izv. RAN. Ser. Mat., 82:2 (2018), 43–78; Izv. Math., 82:2 (2018), 283–317
M. O. Korpusov, A. A. Panin, “On the Nonextendable Solution and Blow-Up of the Solution of the One-Dimensional Equation of Ion-Sound Waves in a Plasma”, Mat. Zametki, 102:3 (2017), 383–395; Math. Notes, 102:3 (2017), 350–360
A. A. Panin, G. I. Shlyapugin, “Local solvability and solution blow-up of one-dimensional equations of the Yajima–Oikawa–Satsuma type”, TMF, 193:2 (2017), 179–192; Theoret. and Math. Phys., 193:2 (2017), 1561–1573
M. O. Korpusov, D. V. Lukyanenko, E. A. Ovsyannikov, A. A. Panin, “Local solvability and decay of the solution of an equation with quadratic noncoercive nonlineatity”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:2 (2017), 107–123
D. V. Luk'yanenko, A. A. Panin, “Blow-up phenomena in the model of a space charge stratification in semiconductors: numerical analysis of original equation reduction to a differential-algebraic system”, Num. Meth. Prog., 17:4 (2016), 437–446
A. A. Panin, “On Local Solvability and Blow-Up of Solutions of an Abstract Nonlinear Volterra Integral Equation”, Mat. Zametki, 97:6 (2015), 884–903; Math. Notes, 97:6 (2015), 892–908
M. O. Korpusov, A. A. Panin, “Blow-up of solutions of an abstract Cauchy problem for a formally hyperbolic equation with double non-linearity”, Izv. RAN. Ser. Mat., 78:5 (2014), 91–142; Izv. Math., 78:5 (2014), 937–985
A. A. Panin, “Local solvability and blowup of the solution of the Rosenau–Bürgers equation with different boundary conditions”, TMF, 177:1 (2013), 93–110; Theoret. and Math. Phys., 177:1 (2013), 1361–1376
M. O. Korpusov, A. A. Panin, “Local solvability and solution blowup for the Benjamin–Bona–Mahony–Burgers equation with a nonlocal boundary condition”, TMF, 175:2 (2013), 159–172; Theoret. and Math. Phys., 175:2 (2013), 580–591
Yu. V. Mukhartova, A. A. Panin, “Blow-up of solutions of an inhomogeneous system of Sobolev-type equations”, Izv. RAN. Ser. Mat., 76:3 (2012), 157–182; Izv. Math., 76:3 (2012), 581–606
16.
Yu. V. Mukhartova, A. A. Panin, “Blow-Up of the Solution of an Inhomogeneous System of Sobolev-Type Equations”, Mat. Zametki, 91:2 (2012), 225–239; Math. Notes, 91:2 (2012), 217–230
A. N. Bogolyubov, M. D. Malykh, A. A. Panin, “Two-sided estimates for the eigenvalues of the Laplace operator with Dirichlet boundary conditions and their application to problems in the mathematical theory of waveguides”, Num. Meth. Prog., 10:1 (2009), 83–93
18.
A. N. Bogolyubov, A. A. Panin, “An error estimate for approximate solutions to elliptic equations with non-coercive bilinear form”, Num. Meth. Prog., 10:1 (2009), 34–48
2008
19.
A. A. Panin, “On the problem of superconvergence of finite element method algorithms”, Zh. Vychisl. Mat. Mat. Fiz., 48:12 (2008), 2180–2185; Comput. Math. Math. Phys., 48:12 (2008), 2211–2216
2005
20.
A. N. Bogolyubov, M. D. Malykh, A. A. Panin, “Time asymptotics of a field excited in a waveguide by a harmonic current”, Zh. Vychisl. Mat. Mat. Fiz., 45:12 (2005), 2219–2231; Comput. Math. Math. Phys., 45:12 (2005), 2135–2147
I. V. Prigorniy, A. A. Panin, D. V. Lukyanenko, “Some features of numerical diagnostics of instantaneous blow-up of the solution by the example of solving the equation of slow diffusion”, Num. Meth. Prog., 22:1 (2021), 77–86
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