scholarly journals The critical Fujita number for a semilinear heat equation in exterior domains with homogeneous Neumann boundary values

2000 ◽  
Vol 130 (3) ◽  
pp. 591-602 ◽  
Author(s):  
H. A. Levine ◽  
Q. S. Zhang
Keyword(s):  
Boundary Value Problem ◽  
Global Solutions ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Boundary Values ◽  
Exterior Domains ◽  
Semilinear Heat Equation ◽  
Image Position ◽  
Initial Boundary Value

Let D be a domain in Rn with bounded complement and let n ≠ 2. For the initial-boundary value problem we prove that there are no non-trivial global (non-negative) solutions if 0 < n (p − 1) ≤ 2 and there exist both global non-trivial and non-global solutions if n (p − 1) > 2.

The wave front set of the solution of a simple initial-boundary value problem with glancing rays. II

1977 ◽  
Vol 81 (1) ◽  
pp. 97-120 ◽  
Author(s):  
F. G. Friedlander ◽  
R. B. Melrose
Keyword(s):  
Boundary Value Problem ◽  
Wave Front ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Principal Result ◽  
Wave Front Set ◽  
Precise Meaning ◽  
Image Position ◽  
Initial Boundary Value

This paper is a sequel to an earlier paper in these Proceedings by one of us ((5); this will be referred to as [I]). The question considered there was that of determining the wave front set of the solution of the boundary value problemwhere x∈+, y∈n, and n > 1; the precise meaning of the boundary condition at x = 0 is explained in section 1 below. The principal result of [I] can be expressed concisely by saying that singularities do not propagate along the boundary; a detailed statement is given in Theorem 1·9 of the present paper.

Energy Decay of Global Solutions for a System of Petrovsky Equations

2013 ◽  
Vol 405-408 ◽  
pp. 3160-3164
Author(s):  
Yao Jun Ye
Keyword(s):  
Boundary Value Problem ◽  
Bounded Domain ◽  
Decay Estimate ◽  
Boundary Value ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Energy Decay ◽  
Difference Inequality ◽  
Initial Boundary Value

The initial-boundary value problem for a class of nonlinear Petrovsky systems in bounded domain is studied. We prove the energy decay estimate of global solutions through the use of a difference inequality.

Existence Theorem for the Initial-Boundary Value Problem for a Singular Parabolic Partial Differential Equation

1972 ◽  
Vol 15 (2) ◽  
pp. 229-234
Author(s):  
Julius A. Krantzberg
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Image Position ◽  
Initial Boundary Value

We consider the initial-boundary value problem for the parabolic partial differential equation1.1in the bounded domain D, contained in the upper half of the xy-plane, where a part of the x-axis lies on the boundary B(see Fig.1).

scholarly journals An iteration method for the determination of an unknown boundary condition in a parabolic initial-boundary value problem

1989 ◽  
Vol 32 (1) ◽  
pp. 59-71 ◽  
Author(s):  
Michael Pilant ◽  
William Rundell
Keyword(s):  
Boundary Value Problem ◽  
Heat Conduction Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Fourth Power ◽  
Unknown Boundary ◽  
The Difference ◽  
Image Position ◽  
Initial Boundary Value

Consider the initial boundary value problemIn the context of the heat conduction problem, this models the case where the heat flux across the ends at the rod is a function of the temperature. If the heat exchange between the rod and its surroundings is purely by convection, then one commonly assumes that f is a linear function of the difference in temperatures between the ends of the rod and that of the surroundings, (Newton's law of cooling). For the case of purely radiative transfer of energy a fourth power law for the function f is usual, (Stefan's law).

Travelling waves in an initial-boundary value problem

1981 ◽  
Vol 90 (1-2) ◽  
pp. 41-61 ◽  
Author(s):  
E. J. M. Veling
Keyword(s):  
Boundary Value Problem ◽  
Asymptotic Expression ◽  
Travelling Waves ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stationary Problem ◽  
Travelling Wave ◽  
Boundary Values ◽  
Initial Boundary Value

SynopsisIn this paper we consider the initial-boundary value problem for the semihnear diffusion equation ul=uxx+f(u) on the half-line x>0, when for 0<a<1 f(0)=f(a)=f(1)=0 and f(u)<0 on (0, a), f(u)>0 on (a, 1). For a wide class of initial and boundary values a uniformly valid asymptotic expression is given to which the solution converges exponentially. This expression is composed of a travelling wave and a solution of the stationary problem.

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