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Yuri Egorov (1996)
Banach Center Publications
An example of a locally unsolvable hyperbolic equation of the second order is constructed, which has smooth () coefficients, but has no solutions in the class of distributions.
Alain Miranville (2012)
Applications of Mathematics
Our aim in this paper is to study the existence of solutions to a phase-field system based on the Maxwell-Cattaneo heat conduction law, with a logarithmic nonlinearity. In particular, we prove, in one and two space dimensions, the existence of a solution which is separated from the singularities of the nonlinear term.
Vaz, P.T., Deo, S.G. (1990)
Journal of Applied Mathematics and Stochastic Analysis
Tomasz Człapiński (1997)
Annales Polonici Mathematici
We seek for classical solutions to hyperbolic nonlinear partial differential-functional equations of the second order. We give two theorems on existence and uniqueness for problems with nonlocal conditions in bounded and unbounded domains.
Popoviciu, Nicolae (2003)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
Alexander Lomtatidze, Jiří Šremr (2012)
Czechoslovak Mathematical Journal
We study the question of the existence, uniqueness, and continuous dependence on parameters of the Carathéodory solutions to the Cauchy problem for linear partial functional-differential equations of hyperbolic type. A theorem on the Fredholm alternative is also proved. The results obtained are new even in the case of equations without argument deviations, because we do not suppose absolute continuity of the function the Cauchy problem is prescribed on, which is rather usual assumption in the existing...
István Fenyö (1987)
Aequationes mathematicae
Ammar Khodja, F., Benabdallah, A., Teniou, D. (1997)
Portugaliae Mathematica
W. G. Anderson, R. G. McLenaghan (1994)
Annales de l'I.H.P. Physique théorique
R. G. McLenaghan (1974)
Annales de l'I.H.P. Physique théorique
Kiguradze, T. (1997)
Memoirs on Differential Equations and Mathematical Physics
N.U. Ahmed (2008)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
In this paper we consider a class of distributed parameter systems (partial differential equations) determined by strongly nonlinear operator valued measures in the setting of the Gelfand triple V ↪ H ↪ V* with continuous and dense embeddings where H is a separable Hilbert space and V is a reflexive Banach space with dual V*. The system is given by dx + A(dt,x) = f(t,x)γ(dt) + B(t)u(dt), x(0) = ξ, t ∈ I ≡ [0,T] where A is a strongly nonlinear operator valued measure...
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