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  1. Zeitschrift für angewandte Mathematik und Physik
  2. Zeitschrift für angewandte Mathematik und Physik : Volume 66
  3. Zeitschrift für angewandte Mathematik und Physik : Volume 66, Issue 6, December 2015
  4. A semilinear parabolic system with a free boundary
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Zeitschrift für angewandte Mathematik und Physik : Volume 67
Zeitschrift für angewandte Mathematik und Physik : Volume 66
Zeitschrift für angewandte Mathematik und Physik : Volume 66, Issue 6, December 2015
P-Laplace thermistor modeling of electrothermal feedback in organic semiconductor devices
Rigidity of planar central configurations
A dual approach in Orlicz spaces for the nonlinear Helmholtz equation
Spectral gaps for periodic piezoelectric waveguides
Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type
Existence of positive solutions to a Laplace equation with nonlinear boundary condition
A reaction–diffusion SIS epidemic model in an almost periodic environment
Isometric immersions via compensated compactness for slowly decaying negative Gauss curvature and rough data
General decay rates for the wave equation with mixed-type damping mechanisms on unbounded domain with finite measure
Existence and multiplicity of solutions for Kirchhoff-type equation with radial potentials in $${\mathbb{R}^{3}}$$ R 3
Global existence and boundedness in a higher-dimensional quasilinear chemotaxis system
Cauchy problems of pseudo-parabolic equations with inhomogeneous terms
Moving boundary problems for the Harry Dym equation and its reciprocal associates
Stabilization and asymptotic behavior of a generalized telegraph equation
The combined non-relativistic and quasi-neutral limit of two-fluid Euler–Maxwell equations
Existence and asymptotic behavior of sign-changing solutions for the nonlinear Schrödinger–Poisson system in $${\mathbb{R}^3}$$ R 3
Regularity of mild Solutions for fractional abstract Cauchy problem with order $${\alpha \in (1, 2)}$$ α ∈ ( 1 , 2 )
Vanishing shear viscosity in the magnetohydrodynamic equations with temperature-dependent heat conductivity
A semilinear parabolic system with a free boundary
Ground-state solution for a class of biharmonic equations including critical exponent
Anisotropic Gagliardo–Nirenberg inequality with fractional derivatives
Asymptotic analysis of random boundary layers between two incompressible viscous fluid flows
Can the water in two communicating wells in an unconfined aquifer oscillate?
Mixed convection boundary layer flow over a horizontal elliptic cylinder with constant heat flux
Poiseuille flow and thermal transpiration of a rarefied gas between parallel plates II: effect of nonuniform surface properties in the longitudinal direction
Axisymmetric rotational stagnation-point flow impinging on a rotating disk
A two-temperature model for thermoelectric effects and its consequences in practical applications
Stability of axisymmetric liquid bridges
Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence
Reinforcement of a Mindlin–Timoshenko plate by a thin layer
Ferromagnetic of nanowires of infinite length and infinite thin films
Thermomechanics of damageable materials under diffusion: modelling and analysis
A mixed variational problem with applications in contact mechanics
Discrete Sommerfeld diffraction problems on hexagonal lattice with a zigzag semi-infinite crack and rigid constraint
On the compatibility equations of nonlinear and linear elasticity in the presence of boundary conditions
Interaction of a screw dislocation with an interface and a nanocrack incorporating surface elasticity
Study of a new class of nonlinear inextensible elastic bodies
Interaction between a piezoelectric screw dislocation and a finite crack with surface piezoelectricity
Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coefficients
TEM wave propagation in a microstrip line on a substrate of circular segment cross section
Zeitschrift für angewandte Mathematik und Physik : Volume 66, Issue 5, October 2015
Zeitschrift für angewandte Mathematik und Physik : Volume 66, Issue 4, August 2015
Zeitschrift für angewandte Mathematik und Physik : Volume 66, Issue 3, June 2015
Zeitschrift für angewandte Mathematik und Physik : Volume 66, Issue 2, April 2015
Zeitschrift für angewandte Mathematik und Physik : Volume 66, Issue 1, February 2015
Zeitschrift für angewandte Mathematik und Physik : Volume 65
Zeitschrift für angewandte Mathematik und Physik : Volume 64
Zeitschrift für angewandte Mathematik und Physik : Volume 63
Zeitschrift für angewandte Mathematik und Physik : Volume 62
Zeitschrift für angewandte Mathematik und Physik : Volume 61
Zeitschrift für angewandte Mathematik und Physik : Volume 60
Zeitschrift für angewandte Mathematik und Physik : Volume 59
Zeitschrift für angewandte Mathematik und Physik : Volume 58
Zeitschrift für angewandte Mathematik und Physik : Volume 57
Zeitschrift für angewandte Mathematik und Physik : Volume 56
Zeitschrift für angewandte Mathematik und Physik : Volume 55
Zeitschrift für angewandte Mathematik und Physik : Volume 54
Zeitschrift für angewandte Mathematik und Physik : Volume 53
Zeitschrift für angewandte Mathematik und Physik : Volume 52
Zeitschrift für angewandte Mathematik und Physik : Volume 51
Zeitschrift für angewandte Mathematik und Physik : Volume 50
Zeitschrift für angewandte Mathematik und Physik : Volume 49
Zeitschrift für angewandte Mathematik und Physik : Volume 48

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A semilinear parabolic system with a free boundary

Content Provider Springer Nature Link
Author Zhao, Yonggang Wang, Mingxin
Copyright Year 2015
Abstract This paper deals with a semilinear parabolic system with reaction terms $${v^p, u^q}$$ and a free boundary $${x = s(t)}$$ in one space dimension, where $${s(t)}$$ evolves according to the free boundary condition $${s'(t) = -\mu(u_x + \rho v_x)}$$ . The main aim of this paper was to study the existence, uniqueness, regularity and long-time behavior of positive solution (maximal positive solution). Firstly, we prove that this problem has a unique positive solution when $${p, q \geq 1}$$ , and a (unique) maximal positive solution when $${p < 1}$$ or $${q < 1}$$ . Then, we study the regularity of $${(u,v)}$$ and $${s}$$ . At last, we discuss the global existence, finite-time blowup of the unique positive solution (maximal positive solution) and long-time behavior of bounded global solution.
Ending Page 3332
Page Count 24
Starting Page 3309
File Format PDF
ISSN 00442275
e-ISSN 14209039
Journal Zeitschrift für angewandte Mathematik und Physik
Issue Number 6
Volume Number 66
Language English
Publisher Springer International Publishing
Publisher Date 2015-09-10
Publisher Place Cham
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Free boundary Parabolic system Free boundary problems Blowup Theoretical and Applied Mechanics Long-time behavior Asymptotic behavior of solutions Uniqueness problems: global uniqueness, local uniqueness, non-uniqueness Existence problems: global existence, local existence, non-existence Mathematical Methods in Physics Global existence Regularity Initial-boundary value problems for second-order parabolic systems
Content Type Text
Resource Type Article
Subject Applied Mathematics Physics and Astronomy
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