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Items by Galaktionov, Victor

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Number of items: 56.

2014

Galaktionov, V. A., Mitidieri, E. and Pohozaev, S.I., 2014. Classification of global and blow-up sign-changing solutions of a semilinear heat equation in the subcritical fujita range : Second-order diffusion. Advanced Nonlinear Studies, 14 (1), pp. 1-29.

Álvarez-Caudevilla, P. and Galaktionov, V. A., 2014. Forthcoming. Well-posedness of the Cauchy problem for a fourth-order thin film equation via regularization approaches. Nonlinear Analysis: Theory Methods & Applications

2013

Álvarez-Caudevilla, P., Evans, J. D. and Galaktionov, V. A., 2013. The Cauchy problem for a tenth-order thin film equation I. Bifurcation of oscillatory fundamental solutions. Mediterranean Journal of Mathematics, 10 (4), pp. 1761-1792.

2012

Fernandes, R. S. and Galaktionov, V. A., 2012. Eigenfunctions and very singular similarity solutions of odd-order nonlinear dispersion PDEs : Toward a "nonlinear Airy function" and others. Studies in Applied Mathematics, 129 (2), pp. 163-219.

Galaktionov, V. A. and Maz'ya, V., 2012. Boundary characteristic point regularity for Navier-Stokes equations: Blow-up scaling and Petrovskii-type criterion (a formal approach). Nonlinear Analysis: Theory Methods & Applications, 75 (12), pp. 4534-4559.

Galaktionov, V.A., Mitidieri, E. and Pohozaev, S.I., 2012. Global sign-changing solutions of a higher order semilinear heat equation in the subcritical fujita range. Advanced Nonlinear Studies, 12 (3), pp. 569-596.

2011

Alvarez-Caudevilla, P. and Galaktionov, V. A., 2011. Local bifurcation-branching analysis of global and "blow-up" patterns for a fourth-order thin film equation. NoDEA-Nonlinear Differential Equations and Applications, 18 (5), pp. 483-537.

Galaktionov, V. A., Mitidieri, E. and Pohozaev, S. I., 2011. Variational approach to complicated similarity solutions of higher-order nonlinear PDEs. II. Nonlinear Analysis: Real World Applications, 12 (4), pp. 2435-2466.

Evans, J. D. and Galaktionov, V. A., 2011. On continuous branches of very singular similarity solutions of a stable thin film equation. I - The Cauchy problem. European Journal of Applied Mathematics, 22 (3), pp. 217-243.

Evans, J. D. and Galaktionov, V. A., 2011. On continuous branches of very singular similarity solutions of the stable thin film equation. II - Free-boundary problems. European Journal of Applied Mathematics, 22 (3), pp. 245-265.

Galaktionov, V. A., 2011. Single point gradient blow-up and nonuniqueness for a third-order nonlinear dispersion equation. Studies in Applied Mathematics, 126 (2), pp. 103-143.

Galaktionov, V. and Svirshchevskii, S. R., 2011. Invariant solutions of nonlinear diffusion equations with maximal symmetry algebra. Journal of Nonlinear Mathematical Physics, 18, pp. 107-121.

2010

Galaktionov, V. A. and Kamotskiy, I. V., 2010. On nonexistence of Baras-Goldstein type for higher-order parabolic equations with singular potentials. Transactions of the American Mathematical Society, 362 (8), pp. 4117-4136.

Chaves, M. and Galaktionov, V. A., 2010. On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation, I: Local oscillatory properties. Nonlinear Analysis: Theory Methods & Applications, 72 (11), pp. 4030-4048.

Galaktionov, V. A., 2010. Incomplete self-similar blow-up in a semilinear fourth-order reaction-diffusion equation. Studies in Applied Mathematics, 124 (4), pp. 347-381.

Galaktionov, V., 2010. Shock waves and compactons for fifth-order non-linear dispersion equations. European Journal of Applied Mathematics, 21 (1), pp. 1-50.

Galaktionov, V. A., 2010. Very singular solutions for thin film equations with absorption. Studies in Applied Mathematics, 124 (1), pp. 39-63.

Galaktionov, V. A., 2010. Vast multiplicity of very singular self-similar solutions of a semilinear higher-order diffusion equation with time-dependent absorption. Journal of Mathematical Sciences-the University of Tokyo, 17 (4), pp. 323-358.

2009

Galaktionov, V. A., 2009. Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach. Nonlinearity, 22 (7), pp. 1695-1741.

Galaktionov, V. A., Mitidieri, E. and Pohozaev, S. I., 2009. On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations. Nonlinear Analysis: Theory Methods & Applications, 70 (8), pp. 2930-2952.

Galaktionov, V. A., 2009. On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach. NoDEA-Nonlinear Differential Equations and Applications, 16 (5), pp. 597-655.

Galaktionov, V. A., 2009. The formation of shocks and fundamental solution of a fourth-order quasilinear Boussinesq-type equation. Nonlinearity, 22 (2), pp. 239-257.

Galaktionov, V. A., 2009. Three types of self-similar blow-up for the fourth-order p-Laplacian equation with source. Journal of Computational and Applied Mathematics, 223 (1), pp. 326-355.

2008

Galaktionov, V. A., 2008. Nonlinear Dispersion Equations: Smooth Deformations, Compactions, and Extensions to Higher Orders. Computational Mathematics and Mathematical Physics, 48 (10), pp. 1823-1856.

Galaktionov, V. A. and Pohozaev, S. I., 2008. Third-Order Nonlinear Dispersive Equations: Shocks, Rarefaction, and Blowup Waves. Computational Mathematics and Mathematical Physics, 48 (10), pp. 1784-1810.

Galaktionov, V., Mitidieri, E. and Pohozaev, S. I., 2008. Capacity induced by a nonlinear operator and applications. Georgian Mathematical Journal, 15 (3), pp. 501-516.

Galaktionov, V. A., 2008. Hermitian Spectral Theory and Blow-Up Patterns for a Fourth-Order Semilinear Boussinesq Equation. Studies in Applied Mathematics, 121 (4), pp. 395-431.

Galaktionov, V. A. and Harwin, P. J., 2008. On Center Subspace Behavior in Thin Film Equations. SIAM Journal on Applied Mathematics, 69 (5), pp. 1334-1358.

Galaktionov, V. A., 2008. On Nonexistence of Baras-Goldstein Type without Positivity Assumptions for Singular Linear and Nonlinear Parabolic Equations. Proceedings of the Steklov Institute of Mathematics, 260 (1), pp. 123-143.

Galaktionov, V., 2008. On higher-order viscosity approximations of odd-order nonlinear PDEs. Journal of Engineering Mathematics, 60 (2), pp. 173-208.

2007

Galaktionov, V. A. and Svirshchevskii, S. R., 2007. Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics. Boca Raton, FL.: Chapman Hall/CRC. (Chapman & Hall/CRC Applied Mathematics and Nonlinear Science)

2006

Galaktionov, V. A. and Pohozaev, S. I., 2006. Blow-up and critical exponents for parabolic equations with non-divergent operators: dual porous medium and thin film operators. Journal of Evolution Equations, 6, 45--69.

Evans, J. D., Galaktionov, V. A. and Williams, J. F., 2006. Blow-up and global asymptotics of the unstable Cahn-Hilliard equation with a homogeneous nonlinearity. Siam Journal on Mathematical Analysis, 38, 64--102.

2005

Galaktionov, V. A., 2005. On extensions of Hardy's inequalities. Communications in Contemporary Mathematics, 7, 97--120.

Galaktionov, V. A. and Shishkov, A. E., 2005. Self-similar boundary blow-up for higher-order quasilinear parabolic equations. Proceedings of the Royal Society of Edinburgh Section A - Mathematics, 135, 1195--1227.

Galaktionov, V. A. and King, J. R., 2005. Stabilization to a singular steady state for the Frank-Kamenetskii equation in a critical dimension. Proceedings of the Royal Society of Edinburgh Section A - Mathematics, 135, 777--787.

2004

Galaktionov, V. A. and Shishkov, A. E., 2004. Structure of boundary blow-up for higher-order quasilinear parabolic equations. Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences, 460, 3299--3325.

Galaktionov, V. A., 2004. Evolution completeness of separable solutions of non-linear diffusion equations in bounded domains. Mathematical Methods in the Applied Sciences, 27, 1755--1770.

Chaves, M. and Galaktionov, V. A., 2004. Stability of perturbed nonlinear parabolic equations with Sturmian property. Journal of Functional Analysis, 215, 253--270.

Galaktionov, V. A. and Williams, J. F., 2004. On very singular similarity solutions of a higher-order semilinear parabolic equation. Nonlinearity, 17, 1075--1099.

Galaktionov, V. A., 2004. On higher-order semilinear parabolic equations with measures as initial data. Journal of the European Mathematical Society, 6, 193--205.

Galaktionov, V. A., 2004. Geometric Sturmian theory of nonlinear parabolic equations and applications. Vol. 3. Boca Raton, FL: Chapman & Hall/CRC. (Applied Mathematics and Nonlinear Science Series, 3.)

Budd, C. J., Galaktionov, V. A. and Williams, J. F., 2004. Self-similar blow-up in higher-order semilinear parabolic equations. SIAM Journal on Applied Mathematics, 64 (5), pp. 1775-1809.

2003

Galaktionov, V. A. and Williams, J. F., 2003. Blow-up in a fourth-order semilinear parabolic equation from explosion-convection theory. European Journal of Applied Mathematics, 14, 745--764.

Galaktionov, V. A. and Pohozaev, S. I., 2003. On similarity solutions and blow-up spectra for a semilinear wave equation. Quarterly of Applied Mathematics, 61, 583--600.

Chaves, M. and Galaktionov, V. A., 2003. On uniqueness and stability of self-similar blow-up solutions of nonlinear heat equations: Evolution approach. Communications in Contemporary Mathematics, 5, 329--348.

Galaktionov, V. A. and Pohozaev, S. I., 2003. Blow-up and critical exponents for nonlinear hyperbolic equations. Nonlinear Analysis: Theory Methods & Applications, 53, p. 453.

Galaktionov, V. A. and King, J. R., 2003. Composite structure of global unbounded solutions of nonlinear heat equations with critical Sobolev exponents. Journal of Differential Equations, 189, 199--233.

Galaktionov, V. A. and Shishkov, A. E., 2003. Saint-Venant's principle in blow-up for higher-order quasilinear parabolic equations. Proceedings of the Royal Society of Edinburgh Section A - Mathematics, 133, 1075--1119.

2002

Egorov, Y. V., Galaktionov, V. A., Kondratiev, V. A. and Pohozaev, S. I., 2002. On the asymptotics of global solutions of higher-order semilinear parabolic equations in the supercritical range. Comptes Rendus Mathematique, 335, 805--810.

Ferreira, R., Galaktionov, V. A. and Vazquez, J. L., 2002. Uniqueness of asymptotic profiles for an extinction problem. Nonlinear Analysis: Theory Methods & Applications, 50, p. 495.

Galaktionov, V. A. and Vazquez, J. L., 2002. The problem of blow-up in nonlinear parabolic equations. Discrete and Continuous Dynamical Systems, 8, 399--433.

Galaktionov, V. A. and King, J. R., 2002. Fast diffusion equation with critical Sobolev exponent in a ball. Nonlinearity, 15, 173--188.

Galaktionov, V. A. and Pohozaev, S. I., 2002. Existence and blow-up for higher-order semilinear parabolic equations: Majorizing order-preserving operators. Indiana University Mathematics Journal, 51, 1321--1338.

2001

Chaves, M. and Galaktionov, V. A., 2001. Regional blow-up for a higher-order semilinear parabolic equation. European Journal of Applied Mathematics, 12, 601--623.

Galaktionov, V. A., 2001. On a spectrum of blow-up patterns for a higher-order semilinear parabolic equation. Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences, 457, 1623--1643.

This list was generated on Fri Oct 31 15:48:44 2014 GMT.