共查询到20条相似文献,搜索用时 15 毫秒
1.
We are interested in parabolic problems with L1 data of the type
with i, j=0, 1, (i, j) (0, 0), 0 = 0 and 1 = 1. Here, is an open bounded subset of
with regular boundary and
is a Caratheodory function satisfying the classical Leray-Lions conditions and is a monotone graph in
with closed domain and such that
We study these evolution problems from the point of view of semi-group theory, then we identify the generalized solution of the associated Cauchy problem with the entropy solution of
in the usual sense introduced in [5]. 相似文献
2.
3.
Fengping Yao 《Archiv der Mathematik》2008,90(5):429-439
In this paper we generalize classical L
p
estimates to Orlicz spaces for the parabolic polyharmonic equations. Our argument is based on the iteration-covering procedure.
Received: 10 September 2007 相似文献
4.
K. Janssen 《Potential Analysis》1994,3(4):359-378
Some aspects of multi-parameter potential theory are developed: we give a Choquet-type integral representation for measures which are supermedian for a countable family of submarkovian resolvents of commuting kernels on a Radon measurable space. For the subclass of polysupermedian measures we prove a Riesz-type decomposition, and we show that there is a unique integral representation by minimal polysupermedian measures. The setting covers a variety of very different examples like random fields, measures on product spaces which are supermedian for resolvents on the factor spaces, and completely supermedian measures. 相似文献
5.
Lech Zarȩba 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(4):445-467
In this paper we consider the mixed problem for the equation u
tt
+ A
1
u + A
2(u
t
) + g(u
t
) = f(x, t) in unbounded domain, where A
1 is a linear elliptic operator of the fourth order and A
2 is a nonlinear elliptic operator of the second order. Under natural assumptions on the equation coefficients and f we proof existence of a solution. This result contains, as a special case, some of known before theorems of existence. Essentially,
in difference up to previous results we prove theorems of existence without the additional assumption on behavior of solution
at infinity.
相似文献
6.
Chiara Spina 《Archiv der Mathematik》2008,91(3):265-279
We prove short time pointwise upper bounds for the heat kernels of certain Kolmogorov operators. We use Lyapunov function
techniques, where the Lyapunov functions depend also on the time variable.
Received: 29 November 2007 相似文献
7.
Andrey Shishkov Laurent Véron 《Calculus of Variations and Partial Differential Equations》2008,33(3):343-375
We study the limit behaviour of solutions of with initial data k
δ
0 when k → ∞, where h is a positive nondecreasing function and p > 1. If h(r) = r
β
, β > N(p − 1) − 2, we prove that the limit function u
∞ is an explicit very singular solution, while such a solution does not exist if β ≤ N(p − 1) − 2. If lim
inf
r→ 0
r
2 ln (1/h(r)) > 0, u
∞ has a persistent singularity at (0, t) (t ≥ 0). If , u
∞ has a pointwise singularity localized at (0, 0). 相似文献
8.
9.
Pavol Quittner 《Mathematische Annalen》2001,320(2):299-305
We prove universal a priori estimates of global positive solutions of the parabolic problem in , on . Here is a bounded domain in , , and p < 5 if n=3.
Received April 6, 2000 / Accepted September 21, 2000 / Published online February 5, 2001 相似文献
10.
Jan Jankowski 《Rendiconti del Circolo Matematico di Palermo》2006,55(1):95-102
We show the existence of absolutely continuous extremal solutions to the problemx′(t)=f(t, x)h(t)))+g(t)),x(0)=x
0, whereh is an arbitrary continuous deviated argument. Conditions for the uniqueness of solutions are given.
Research partialy supported by grant UG BW 5100 - 5 - 0143 - 4 相似文献
11.
We obtain existence results for some strongly nonlinear Cauchy problems posed in
and having merely locally integrable data. The equations we deal with have as principal part a bounded, coercive and pseudomonotone
operator of Leray-Lions type acting on
, they contain absorbing zero order terms and possibly include first order terms with natural growth. For any p > 1 and under
optimal growth conditions on the zero order terms, we derive suitable local a-priori estimates and consequent global existence
results. 相似文献
12.
Giovanni Cimatti 《Annali di Matematica Pura ed Applicata》2002,181(2):181-212
The stability of the stationary solution of the thermistor as a circuit element is studied using a Liapunov functional and
the Hale–LaSalle invariance principle. The asymptotic stability of a class of periodic solutions is also considered.
Received: November 22, 1999; in final form: May 23, 2001?Published online: May 29, 2002 相似文献
13.
Our first basic model is the fully nonlinear dual porous medium equation with source
for which we consider the Cauchy problem with given nonnegative bounded initial data u0. For the semilinear case m=1, the critical exponent
was obtained by H. Fujita in 1966. For p ∈(1, p0] any nontrivial solution blows up in finite time, while for p > p0 there exist sufficiently small global solutions. During last thirty years such critical exponents were detected for many
semilinear and quasilinear parabolic, hyperbolic and elliptic PDEs and inequalities. Most of efforts were devoted to equations
with differential operators in divergent form, where classical techniques associated with weak solutions and integration by
parts with a variety of test functions can be applied. Using this fully nonlinear equation, we propose and develop new approaches
to calculating critical Fujita exponents in different functional settings.
The second models with a “semi-divergent” diffusion operator is the thin film equation with source
for which the critical exponent is shown to be
相似文献
14.
In the frame of standard H-cones of functions (the cone of all excessive functions with respect to a submarkovian resolvent of kernels with reference measure on a measurable space) on a Green set we show that the cofine closure of the complement of an absorbent set in coabsorbent. We obtain different characterizations concerning the parabolicity, ellipticity and quasiellipticity in terms of the Green function. We also show that these notions are the same in the direct and the dual theory. 相似文献
15.
Luigi Manca 《Journal of Evolution Equations》2008,8(2):231-262
We consider a semigroup of operators in the Banach space C
b
(H) of uniformly continuous and bounded functions on a separable Hilbert space H. We prove an existence and uniqueness result for a measure valued equation involving this class of semigroups. Then we apply
the result to the transition semigroup and the Kolmogorov operator corresponding to a stochastic PDE in H. For this purpose, we characterize the generator of the transition semigroup on a core.
相似文献
16.
Let X be a Green domain in Rd, d?2, x∈X, and let Mx(P(X)) denote the compact convex set of all representing measures for x. Recently it has been proven that the set of harmonic measures , U open in X, x∈U, which is contained in the set of extreme points of Mx(P(X)), is dense in Mx(P(X)). In this paper, it is shown that Mx(P(X)) is not a simplex (and hence not a Poulsen simplex). This is achieved by constructing open neighborhoods U0, U1, U2, U3 of x such that the harmonic measures are pairwise different and . In fact, these measures form a square with respect to a natural L2-structure. Since the construction is mainly based on having certain symmetries, it can be carried out just as well for Riesz potentials, the Heisenberg group (or any stratified Lie algebra), and the heat equation (or more general parabolic situations). 相似文献
17.
M. van den Berg 《Probability Theory and Related Fields》1994,100(4):439-456
LetD be an open, bounded set in euclidean space
m
(m=2, 3, ...) with boundary D. SupposeD has temperature 0 at timet=0, while D is kept at temperature 1 for allt>0. We use brownian motion to obtain estimates for the solution of corresponding heat equation and to obtain results for the asymptotic behaviour ofE
D
(t), the amount of heat inD at timet, ast0+. For the triadic von Koch snowflakeK our results imply that
相似文献
18.
We prove existence of strong solutions of Pucci extremal equations with superlinear growth in Du and unbounded coefficients. We apply this result to establish the weak Harnack inequality for Lp-viscosity supersolutions of fully nonlinear uniformly elliptic PDEs with superlinear growth terms with respect to Du.
相似文献
19.
Zhaoli Liu Jiabao Su Zhi-Qiang Wang 《Calculus of Variations and Partial Differential Equations》2009,35(4):463-480
In this paper, we study existence of nontrivial solutions to the elliptic equation
20.
The authors localize the blow-up points of positive solutions of the systemu
t
=Δu,v
t
=Δv with conditions
at the boundary of a bounded smooth domain Θ under some restrictions off andg and the initial data (Δu
0, Δν0>c>0).
If Θ is a ball, the hypothesis on the initial data can be removed.
Supported by Universidad de Buenos Aires under grant EX071 and CONICET. 相似文献
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