Ahmed Aberqi, Jaouad Bennouna, Hicham Redwane (2014)
Applicationes Mathematicae
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We prove the existence of a renormalized solution to a class of doubly nonlinear parabolic systems.
Kaouther Ammar, Jaouad Bennouna, Hicham Redwane (2014)
Applicationes Mathematicae
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We prove the existence and uniqueness of a renormalized solution for a class of nonlinear parabolic equations with no growth assumption on the nonlinearities.
Pao-Liu Chow (2015)
Banach Center Publications
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The paper is concerned with the problem of existence of explosive solutions for a class of nonlinear parabolic Itô equations. Under some sufficient conditions on the initial state and the coefficients, it is proven by the method of auxiliary functionals that there exist explosive solutions with positive probability. The main results are presented in Theorems 3.1 and 3.2 under different sets of conditions. An example is given to illustrate some application of the second theorem. ...
Liu, Changchun (2006)
Lobachevskii Journal of Mathematics
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Changchun Liu (2013)
Annales Polonici Mathematici
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We consider an initial-boundary problem for a sixth order nonlinear parabolic equation, which arises in oil-water-surfactant mixtures. Using Schauder type estimates and Campanato spaces, we prove the global existence of classical solutions for the problem in two space dimensions.
Ji Liu, Jia-Shan Zheng (2015)
Czechoslovak Mathematical Journal
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We study a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source, under homogeneous Neumann boundary conditions in a smooth bounded domain. By establishing proper a priori estimates we prove that, with both the diffusion function and the chemotaxis sensitivity function being positive, the corresponding initial boundary value problem admits a unique global classical solution which is uniformly bounded. The result of this paper is a generalization of that of...
V. Lj. Kocić (1985)
Matematički Vesnik
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Mikhail Borsuk (2002)
Annales Polonici Mathematici
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We establish exact Schauder estimates of solutions of the transmission problem for linear parabolic second order equations with explicit dependence on the smoothness of the coefficients. Next we apply the estimates to the solvability of the nonlinear transmission problem.
Dimitrios A. Kandilakis, Manolis Magiropoulos (2006)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We provide an existence result for a system of quasilinear equations subject to nonlinear boundary conditions on a bounded domain by using the fibering method.
Octavia Bolojan, Gennaro Infante, Radu Precup (2015)
Mathematica Bohemica
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The purpose of the present paper is to study the existence of solutions to initial value problems for nonlinear first order differential systems subject to nonlinear nonlocal initial conditions of functional type. The approach uses vector-valued metrics and matrices convergent to zero. Two existence results are given by means of Schauder and Leray-Schauder fixed point principles and the existence and uniqueness of the solution is obtained via a fixed point theorem due to Perov. Two examples...
D. R. Dunninger, Haiyan Wang (1998)
Annales Polonici Mathematici
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We study the existence and multiplicity of positive solutions of the nonlinear equation u''(x) + λh(x)f(u(x)) = 0 subject to nonlinear boundary conditions. The method of upper and lower solutions and degree theory arguments are used.
Korpusov, M.O., Sveshnikov, A.G. (2005)
Sibirskij Matematicheskij Zhurnal
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Uraltseva, N. N.
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Lamberto Cesari (1984)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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We continue here the discussion in part I, and we state and prove further sufficient conditions for the existence of a solution to nonselfadjoint problems.