Existence of extremal periodic solutions for quasilinear parabolic equations
Abstract and Applied Analysis, 1997 In this paper we consider a quasilinear parabolic equation in a bounded domain under periodic Dirichlet boundary conditions. Our main goal is to prove the existence of extremal solutions among all solutions lying in a sector formed by appropriately ...
Siegfried Carl
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On a quasilinear parabolic integrodifferential equation
Differential and Integral Equations, 1995 The author considers the nonlinear Volterra integrodifferential equation \(u_ t - a* \text{div} h(\text{grad} u) = a*g\), where \(x \in \mathbb{R}^ n\), \(t \geq 0\) and where the initial function \(u(0,x) = w(x)\) is given. The kernel \(a\) satisfies \(a \in L^ 1_{\text{loc}} (\mathbb{R}^ +)\) and the parabolic condition \(\text{Re}\widetilde a ...
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Remarks on global solutions to the initial-boundary value problem for quasilinear degenerate parabolic equations with a nonlinear source term [PDF]
Opuscula Mathematica, 2019 We give an existence theorem of global solution to the initial-boundary value problem for \(u_{t}-\operatorname{div}\{\sigma(|\nabla u|^2)\nabla u\}=f(u)\) under some smallness conditions on the initial data, where \(\sigma (v^2)\) is a positive ...
Mitsuhiro Nakao
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Weak solutions to a multi-phase field system of parabolic equations related to alloy solidification [PDF]
, 2007 Existence of weak solutions to a phase field model for solidification of alloys is studied. The model consists of balance equations for the energy and the concentrations of the alloy components which are coupled to a system of Allen-Cahn equations ...
Stinner, Björn
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A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets [PDF]
We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modelling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable ...
Ansgar Jüngel, Bertram Düring
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A multiplicity result for a class of quasilinear elliptic and parabolic problems
Electronic Journal of Differential Equations, 1997 We prove the existence of infinitely many solutions for a class of quasilinear elliptic and parabolic equations, subject respectively to Dirichlet and Dirichlet-periodic boundary conditions.
M. R. Grossinho, Pierpaolo Omari
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Advances in Difference Equations, 2010 We consider the quasilinear parabolic equation with inhomogeneous term , , where , , , , and , . In this paper, we investigate the critical exponents of this equation.
Kobayashi Yasumaro
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Electronic Journal of Differential Equations, 1996 initial data are established for a quasilinear functional reaction-diffusion equation which arises from a two-dimensional energy balance climate model.
Georg Hetzer
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High-Order Difference Scheme for Time-Fractional Quasilinear Parabolic Equations
MathematicsMathematical modeling of heat and mass transfer processes in porous media using fractional derivative equations is of great practical importance. Within the framework of such models, obtaining analytical solutions to the corresponding initial–boundary ...
Miglena N. Koleva, Lubin G. Vulkov
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Existence of Solutions for Quasilinear Parabolic Equations With Nonlocal Boundary Conditions
, 2015 "We prove the existence of a generalized solution a quasilinear parabolic equation with nonlocal boundary conditions, using the Faedo-Galerkin approximation.
Chen, Baili
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