Found 99 Documents (Results 1–99)
Global bounded classical solutions to a parabolic-elliptic chemotaxis model with local sensing and asymptotically unbounded motility. (English) Zbl 1543.35091
Reviewer: Neng Zhu (Nanchang)
Vanishing-spreading dichotomy in a two-species chemotaxis competition system with a free boundary. (English) Zbl 1533.35373
Reviewer: Takashi Suzuki (Ōsaka)
Large self-similar solutions of the parabolic-elliptic Keller-Segel model. (English) Zbl 1523.35263
Reviewer: Eugene Postnikov (Kursk)
Classical solutions to Cauchy problems for parabolic-elliptic systems of Keller-Segel type. (English) Zbl 1523.35268
Reviewer: Piotr Biler (Wrocław)
Existence and boundedness of solutions for a parabolic-elliptic predator-prey chemotaxis system. (English) Zbl 1517.35005
On the existence of global smooth solutions to the parabolic-elliptic Keller-Segel system with irregular initial data. (English) Zbl 1516.35423
Blow-up prevention by logistic source an N-dimensional parabolic-elliptic predator-prey system with indirect pursuit-evasion interaction. (English) Zbl 1501.35095
On a generalized volume-filling chemotaxis system with nonlinear signal production. (English) Zbl 1497.35070
Reviewer: Johannes Lankeit (Hannover)
Error estimates and blow-up analysis of a finite-element approximation for the parabolic-elliptic Keller-Segel system. (English) Zbl 1485.65102
Global existence and decay estimates for the classical solution of fractional attraction-repulsion chemotaxis system. (English) Zbl 1486.92019
Reviewer: Piotr Biler (Wrocław)
Boundedness of solutions to an attraction-repulsion chemotaxis model in \(\mathbb{R}^2\). (English) Zbl 1484.35360
Reviewer: Piotr Biler (Wrocław)
Stability of constant steady states of a chemotaxis model. (English) Zbl 1487.35056
Reviewer: Anna Zhigun (Belfast)
Well-posedness and unconditional uniqueness of mild solutions to the Keller-Segel system in uniformly local spaces. (English) Zbl 1483.35290
Reviewer: Piotr Biler (Wrocław)
Well-posedness, optimal control, and sensitivity analysis for a class of differential variational-hemivariational inequalities. (English) Zbl 1478.49022
Global existence and eventual smoothness in a 2-D parabolic-elliptic system arising from ion transport networks. (English) Zbl 1477.35287
A blow-up result for the chemotaxis system with nonlinear signal production and logistic source. (English) Zbl 1467.92044
Reviewer: Piotr Biler (Wrocław)
Generalized penalty and regularization method for differential variational-hemivariational inequalities. (English) Zbl 1533.47052
Finite-time blow-up prevention by logistic source in parabolic-elliptic chemotaxis models with singular sensitivity in any dimensional setting. (English) Zbl 1455.35269
A cross-diffusive evolution system arising from biological transport networks. (English) Zbl 1452.35221
Global well-posedness of advective Lotka-Volterra competition systems with nonlinear diffusion. (English) Zbl 1465.35276
Reviewer: Thomas Giletti (Vandœuvre-lès-Nancy)
The carrying capacity to chemotaxis system with two species and competitive kinetics in \(N\) dimensions. (English) Zbl 1446.35233
Reviewer: Piotr Biler (Wrocław)
Global existence for Laplace reaction-diffusion equations. (English) Zbl 1445.37053
Reviewer: Boris A. Malomed (Tel Aviv)
Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity. (English) Zbl 1439.35486
Reviewer: Piotr Biler (Wrocław)
Global existence and decay estimates of solutions of a parabolic-elliptic-parabolic system for ion transport networks. (English) Zbl 1442.35364
Classical solution of a PDE system stemming from auxin transport model for leaf venation. (English) Zbl 1439.35494
A refined criterion and lower bounds for the blow-up time in a parabolic-elliptic chemotaxis system with nonlinear diffusion. (English) Zbl 1437.35674
Reviewer: Piotr Biler (Wrocław)
Singularities of solutions to chemotaxis systems. (English) Zbl 1450.35001
De Gruyter Series in Mathematics and Life Sciences 6. Berlin: De Gruyter (ISBN 978-3-11-059789-9/hbk; 978-3-11-059953-4/ebook). xxiv, 205 p. (2020).
Reviewer: Christian Stinner (Darmstadt)
Difference methods to one and multidimensional interdiffusion models with Vegard rule. (English) Zbl 1473.65094
On the blow-up criterion and global existence of a nonlinear PDE system in biological transport networks. (English) Zbl 1420.35440
Global classical solutions, stability of constant equilibria, and spreading speeds in attraction-repulsion chemotaxis systems with logistic source on \(\mathbb{R}^{N}\). (English) Zbl 1426.35035
Reviewer: Piotr Biler (Wrocław)
Parabolic-elliptic chemotaxis model with space-time-dependent logistic sources on \(\mathbb{R}^N\). I: Persistence and asymptotic spreading. (English) Zbl 1426.35034
Reviewer: Piotr Biler (Wrocław)
Boundedness in a four-dimensional attraction-repulsion chemotaxis system with logistic source. (English) Zbl 1394.35232
Capacity solution to a coupled system of parabolic-elliptic equations in Orlicz-Sobolev spaces. (English) Zbl 1391.35233
Positivity of self-similar solutions of doubly nonlinear reaction-diffusion equations. (English) Zbl 1339.35073
Boundedness of solutions to parabolic-elliptic Keller-Segel systems with signal-dependent sensitivity. (English) Zbl 1329.35011
Reviewer: Christian Stinner (München)
On one kind of controllability property of a nonlinear chemotaxis system. (Chinese. English summary) Zbl 1313.92020
A generalized Buckley-Leverett system. (English) Zbl 1280.35073
Chen, Gui-Qiang G. (ed.) et al., Hyperbolic conservation laws and related analysis with applications. Selected papers based on the presentations at the workshop at the International Centre for Mathematical Sciences (ICMS) Edinburgh, UK, September 19–23, 2011. Berlin: Springer (ISBN 978-3-642-39006-7/hbk; 978-3-642-39007-4/ebook). Springer Proceedings in Mathematics & Statistics 49, 87-94 (2014).
Analysis of a non-uniformly elliptic and nonlinear coupled parabolic-elliptic system arising in steel hardening. (English) Zbl 1288.35470
Cross diffusion and nonlinear diffusion preventing blow up in the Keller-Segel model. (English) Zbl 1263.35131
Reviewer: Gabriela Marinoschi (Bucharest)
Null controllability of a degenerated reaction-diffusion system in cardiac electro-physiology. (English. French summary) Zbl 1246.93018
Strong well-posedness of a three phase problem with nonlinear transmission condition. (English) Zbl 1235.35174
Cross diffusion preventing blow-up in the two-dimensional Keller-Segel model. (English) Zbl 1259.35114
SIAM J. Math. Anal. 43, No. 2, 997-1022 (2011); corrigendum ibid. 52, No. 2, 2198-2200 (2020).
Reviewer: Sebastian Anita (Iaşi)
Global existence and decay estimates of solutions to a parabolic-elliptic system of drift-diffusion type in \(\mathbb R^2\). (English) Zbl 1240.35066
Reviewer: Hana Petzeltová (Praha)
Global asymptotics toward the rarefaction waves for a parabolic-elliptic system related to the Camassa-Holm shallow water equation. (English) Zbl 1199.35255
Global existence of solutions for a nonlinearly perturbed Keller-Segel system in \(\mathbb R^2\). (English) Zbl 1182.35037
Reviewer: Philippe Laurençot (Toulouse)
Existence of periodic solutions for the thermistor problem with the Joule-Thomson effect. (English) Zbl 1180.35039
Nonlinear diffusion models for self-gravitating particles. (English) Zbl 1113.35328
Figueiredo, Isabel Narra (ed.) et al., Free boundary problems. Theory and applications. Based on the lectures and communications presented at the free boundary problems conference (FBP 2005), Coimbra, Portugal, June 7–12, 2005. Basel: Birkhäuser (ISBN 3-7643-7718-6/hbk). ISNM. International Series of Numerical Mathematics 154, 107-116 (2007).
Weak-\(L^p\) solutions for a model of self-gravitating particles with an external potential. (English) Zbl 1113.35030
Existence and uniqueness of a classical solution of Fourier’s first problem for nonlinear parabolic-elliptic systems. (English) Zbl 1221.35432
Reviewer: Panagiotis Ch. Tsamatos (Ioannina)
MSC:
35R10
On the existence of periodic solutions in the thermistor problem with degenerate thermal conductivity. (English) Zbl 1107.35311
On some parabolic-elliptic system with self-similar pressure term. (English) Zbl 1110.35090
Biler, Piotr (ed.) et al., Self-similar solutions of nonlinear PDE. Selected papers of the conference, Bȩdlewo, Poland, September 5–9, 2005. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 74, 205-215 (2006).
An existence result for a nonlinear parabolic-elliptic problem. (English) Zbl 1090.35008
Simos, Theodore S. (ed.) et al., ICNAAM 2005. International conference on numerical analysis and applied mathematics 2005. Official conference of the European Society of Computational Methods in Sciences and Engineering (ESCMSE), Rhodes, Greek, September 16–20, 2005. Weinheim: Wiley-VCH (ISBN 3-527-40652-2/hbk). 214-217 (2005).
Global existence and blow-up for the solutions to nonlinear parabolic-elliptic system modelling chemotaxis. (English) Zbl 1103.35039
Reviewer: Dirk Horstmann (Köln)
A model of evolution of temperature and density of ions in an electrolyte. (English) Zbl 1075.35015
Reviewer: Georg V. Jaiani (Tbilisi)
Self-similar blow up for a diffusion-attraction problem. (English) Zbl 1067.35134
Reviewer: Ilya A. Chernov (Petrozavodsk)
Optimal boundary control of glass cooling processes. (English) Zbl 1049.35044
Reviewer: Gheorghe Aniculăesei (Iaşi)
On the solvability of H. Amann’s problem in Hölder spaces. (English. Russian original) Zbl 1082.35074
J. Math. Sci., New York 127, No. 2, 1828-1848 (2005); translation from Zap. Nauchn. Semin. POMI 295, 18-56 (2003).
Reviewer: Messoud A. Efendiev (Berlin)
Existence of weak solutions to a system of avalanche-semiconductor equations. (English) Zbl 1029.35117
The evolution thermistor problem with degenerate thermal conductivity. (English) Zbl 1012.35047
Reviewer: Dian K.Palagachev (Bari)
Dynamics of the convergence towards a self-similar blowup solution in a simplified model of aggregation. (English) Zbl 1012.35008
Reviewer: Emil Minchev (Chiba)
General pointwise relations for the relative rearrangement and applications. (English) Zbl 1034.35037
Quasi-hydrodynamic semiconductor equations. (English) Zbl 0969.35001
Progress in Nonlinear Differential Equations and their Applications. 41. Basel: Birkhäuser. x, 293 p. (2001).
Reviewer: Joachim Naumann (Berlin)
The local solution of a parabolic-elliptic equation with a nonlinear Neumann boundary condition. (English) Zbl 1060.35528
Reviewer: Hana Petzeltová (Praha)
A finite-difference method for a non-linear parabolic-elliptic system with Dirichlet conditions. (English) Zbl 0996.65085
Diffusion, attraction and collapse. (English) Zbl 0942.35018
Reviewer: Grzegorz Karch (Wrocław)
Self-interaction of Brownian particles coupled with thermodynamic processes. (English) Zbl 1010.82028
A nonlocal singular parabolic problem modelling gravitational interaction of particles. (English) Zbl 0952.35008
Reviewer: Dimitar A.Kolev (Sofia)
Asymptotic behavior of the solution to a nonisentropic hydrodynamic model of semiconductors. (English) Zbl 0913.35060
Reviewer: J.Naumann (Berlin)
A singular radially symmetric problem in electrolytes theory. (English) Zbl 0919.35020
Reviewer: J.Naumann (Berlin)
Nonlinear singular parabolic equations. (English) Zbl 0912.35090
Caristi, Gabriella et al., Reaction diffusion systems. Papers from a meeting, Trieste, Italy, October 2–7, 1995. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 194, 21-36 (1998).
Reviewer: M.Kopáčková (Praha)
A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects. (English) Zbl 0907.35059
Reviewer: J.Naumann (Berlin)
A singular problem in electrolytes theory. (English) Zbl 0885.35051
Reviewer: A.Cichocka (Katowice)
Computational differential equations. (English) Zbl 0946.65049
Cambridge: Cambridge Univ. Press. xvi, 538 p. (1996).
Reviewer: I. P. Gavrilyuk (MR 97m:65006)
The Cauchy problem and self-similar solutions for a nonlinear parabolic equation. (English) Zbl 0829.35044
Reviewer: H.Marcinkowska (Wrocław)
Existence and nonexistence of solutions for a model of gravitational interaction of particles. III. (English) Zbl 0836.35076
Existence and nonexistence of solutions for a model of gravitational interaction of particles. II. (English) Zbl 0832.35015
Reviewer: D.Palagachev (Sofia)
Existence and nonexistence of solutions for a model of gravitational interaction of particles. I. (English) Zbl 0817.35041
Reviewer: D.Palagachev (Sofia)
Existence and asymptotics of solutions for a parabolic-elliptic system with nonlinear no-flux boundary conditions. (English) Zbl 0781.35025
Reviewer: P.A.McCoy (Annapolis)
Chemical interfacial reaction models with radial symmetry. (English) Zbl 0792.35001
Nonlinear diffusion equations and their equilibrium states, Proc. 3rd Conf., Gregynog/UK 1989, Prog. Nonlinear Differ. Equ. Appl. 7, 561-572 (1992).
Finite element variational crimes in parabolic-elliptic problems. I: Nonlinear schemes. (English) Zbl 0673.65071
Reviewer: V.V.Kobkov
Variational inequality formulation and optimal control of nonlinear evolution systems governed by free boundary problems. (English) Zbl 0506.35062
Applied nonlinear functional analysis, variational methods and ill-posed problems, Proc. Workshop, Berlin 1981, Meth. Verf. Math. Phys. 25, 213-250 (1983).
A variational inequality approach to generalized two-phase Stefan problem in several space variables. (English) Zbl 0506.35061
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