共查询到20条相似文献,搜索用时 15 毫秒
1.
Gustavo Ponce 《Annali di Matematica Pura ed Applicata》1987,148(1):17-28
Summary The initial value problem for a nonlinear nonuniform parabolic equation is studied The coefficient of the nonlinear term is defined by the operator (–)/2. The goal is to prove the global existence of a smooth solution for any smooth initial data. Conditions which guarantee the above result are given. They involve the parameter and the dimension n. 相似文献
2.
A. M. El-Sayed 《Periodica Mathematica Hungarica》1988,19(2):143-147
In the present work it is studied the initial value problem for an equation in the form
相似文献
3.
Linghai Zhang 《应用数学学报(英文版)》1992,8(4):367-376
We study the initial value problem for a nonlinear parabolic equation with singular integral-differential term. By means of a series of a priori estimations of the solutions to the problem and Leray-Schauder fixed point principle, we demonstrate the existence and uniqueness theorems of the generalized and classical global solutions. Lastly, we discuss the asymptotic properties of the solution ast tends to infinity. 相似文献
4.
5.
Neil Kenneth Bedingfield 《Aequationes Mathematicae》1980,20(1):90-96
We consider the functional equationf(A(x,y))=B(f(x),f(y)), whereA andB are averages. It is known that such a functional equation has exactly one continuous solution satisfying a given two-point condition. By analogy with the theory of differential equations, we may regard the functional equation, together with a two-point condition, as a boundary value problem. (Then each boundary value problem has a unique continuous solution.) If we replace the two-point condition with the specification of a value and derivative at just one point, we obtain an initial value problem.Consider the initial value problemsf(A(x,y))=B(f(x),f(y)),f(a)=s,f(a)=, obtained by fixinga ands and allowing to vary through the set of positive real numbers. The main result of this paper gives a necessary and sufficient condition for each of the initial value problems to have a unique continuous solution, under the hypothesis that at least one of the problems has a continuous solution. This is a partial answer to the problem of determining conditions which are sufficient for the existence of a unique continuous solution of a given initial value problem. 相似文献
6.
7.
Robert Kersner 《Journal of Differential Equations》2004,199(1):47-76
We study well-posedness of initial value problems for a class of singular quasilinear parabolic equations in one space dimension. Simple conditions for well-posedness in the space of bounded nonnegative solutions are given, which involve boundedness of solutions of some related linear stationary problems. By a suitable change of unknown, the above results can be applied to classical initial-boundary value problems for parabolic equations with singular coefficients, as the heat equation with inverse square potential. 相似文献
8.
Qi Zhang 《Transactions of the American Mathematical Society》1996,348(7):2811-2844
We obtain the existence of the weak Green's functions of parabolic equations with lower order coefficients in the so called parabolic Kato class which is being proposed as a natural generalization of the Kato class in the study of elliptic equations. As a consequence we are able to prove the existence of solutions of some initial boundary value problems. Moreover, based on a lower and an upper bound of the Green's function, we prove a Harnack inequality for the non-negative weak solutions.
9.
Shota Sato 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(4):1383-1392
We consider the Cauchy problem for a parabolic partial differential equation with a power nonlinearity. Our concern in this paper is the existence of a singular solution with smooth initial data. By using the Haraux-Weissler equation, it is shown that there exist singular forward self-similar solutions. Using this result, we also obtain a sufficient condition for the singular solution with general initial data including smooth initial data. 相似文献
10.
B. Yu. Irgashev 《Russian Mathematics (Iz VUZ)》2016,60(7):37-46
We study an eigenvalue problem for an equation of even order in a rectangular domain. We investigate distribution and asymptotics of eigenvalues and explore their difference under variation of the potential q(x, y). 相似文献
11.
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.
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12.
Hiroyuki Chihara 《Proceedings of the American Mathematical Society》2005,133(7):2083-2090
We present the necessary and sufficient conditions for the -well-posedness of the initial problem for a third order linear dispersive equation on the two-dimensional torus. Birkhoff's method of asymptotic solutions is used to prove necessity. Some properties of a system for quadratic algebraic equations associated to the principal symbol play a crucial role in proving sufficiency.
13.
An inverse problem for a semilinear parabolic equation 总被引:2,自引:0,他引:2
A. Lorenzi 《Annali di Matematica Pura ed Applicata》1982,131(1):145-166
Summary In this paper we are concerned with the study of the stability of an unknown non-linear term in a parabolic equation in dependence on over specified Cauchy-Dirichlet data prescribed on the parabolic boundary of the open set under consideration. Since, in general, the dependence of the nonlinear term upon the data is not stable with respect to L -metrics, we show how a Hölder continuity may be restored under mild restrictions for the set of admissible solutions.Lavoro eseguito nell'amMto del G.N.A.F.A. del C.N.R. 相似文献
14.
A. Lorenzi 《Annali di Matematica Pura ed Applicata》1985,142(1):145-169
Sunto Si considera un problema parabolico sovraderminato in una sola variabile spaziale per l'operatore quasilineare definito da · a3 o u. Tale operatore contiene un termine incognito a(k {0, 1, 2, 3})del quale si studia la dipendenza dalle condizioni iniziali e alla frontiera. Si determinano due classi, rispettivamente di dati e di soluzioni ammissibili, ed una coppia di metriche rispetto alle quali l'applicazione dati(u, ak)è lipschitziana. Si mostra infine che tale applicazione si mantiene hölderiana quando le metriche ammesse per i dati sono soltanto del tipo L.
Lavoro eseguito con contributo del Ministero della Pubblica Istruzione e nell'ambito del Gruppo G.N.A.F.A. del C.N.R. 相似文献 15.
16.
17.
A singular initial value problem and self-similar solutions of a nonlinear dissipative wave equation
Jianfeng Liang 《Journal of Differential Equations》2009,246(2):819-844
We present a systematic study of local solutions of the ODE of the form near t=0. Such ODEs occur in the study of self-similar radial solutions of some second order PDEs. A general theorem of existence and uniqueness is established. It is shown that there is a dichotomy between the cases γ>0 and γ<0, where γ=∂f/∂x′ at t=0. As an application, we study the singular behavior of self-similar radial solutions of a nonlinear wave equation with superlinear damping near an incoming light cone. A smoothing effect is observed as the incoming waves are focused at the tip of the cone. 相似文献
18.
Sunto Si considera un problema sovradeterminato per l'operatore parabolico semilineare D(u)=Dtu – D
x
2
– a(u) contenente un termine incognito a(u) e si prova l'esistenza di almeno una soluzione (u, a).
Gli autori sono membri del Gruppo Nazionale per l'Analisi Funzionale e le Applicazioni del C.N.R. Lavoro parzialmente finanziato dal Ministero della Pubblica Istruzione. 相似文献 19.
We prove existence and uniqueness theorems for the inverse problem of finding the right-hand side of a higher-order parabolic
equation with two independent variables and an additional condition in the form of integral overdetermination. The results
obtained are used to study the passage to the limit in a sequence of such inverse problems with weakly convergent coefficients.
Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 680–691, November, 1998. 相似文献
20.
《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2020,37(5):1185-1209
We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time solutions and identify the strongest singularity of the initial data for the solvability of the Cauchy problem. 相似文献
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