Results 31 to 40 of about 3,753 (167)
Nonlinear Parabolic Equations with Regularized Derivatives
Journal of Mathematical Analysis and Applications, 1999 Nonlinear systems of differential equations \[ \partial_tu+\partial_xf(u)+g(u)=\Delta u\tag{1} \] are considered on \(\mathbb R_+^{n+1}\) \((t>0)\), where \(u=(u_1,\dots,u_m)^T\), \(f(u)=(f_1(u),\dots,f_n(u))^T\), \(\partial_xf(u)=\sum_{i=1}^n\partial_{x_i}f_i(u)\).
Wang, Y.G., Oberguggenberger, M.
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Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations
Advances in Nonlinear Analysis, 2020 This paper is concerned with the positivity of solutions to the Cauchy problem for linear and nonlinear parabolic equations with the biharmonic operator as fourth order elliptic principal part. Generally, Cauchy problems for parabolic equations of fourth
Grunau Hans-Christoph +2 more
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Bounded Solutions to Nonlinear Parabolic Equations [PDF]
ISRN Mathematical Analysis, 2011 We deal with existence results for nonlinear parabolic equations with general quadratic gradient terms and with absorption term which depend on the solution. We note that no boundedness is assumed on the data of the problem. We prove an existence result of distributional solution via test-function method.
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Optimal Control Problems of a Class of Nonlinear Degenerate Parabolic Equations
MathematicsThe optimal control problems of degenerate parabolic equations have many applications in economics, physics, climatology, and so on. Motivated by the applications, we consider the optimal control problems of a class of nonlinear degenerate parabolic ...
Yang Na +3 more
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Nonlinear Parabolic Equations with Measure Data
Journal of Functional Analysis, 1997 Consider the parabolic problem \[ u_t -\mathop{div} a(x,t,u,Du) = \mu \quad\text{in } Q,\qquad u = 0 \quad \text{on } \mathcal PQ, \] where \(a(x,t,z,\xi)\) behaves like \(|\xi|^{p-2}\xi\), \(Q\) is a space-time cylinder with parabolic boundary \(\mathcal PQ\), and \(\mu\) is a measure on \(Q\).
BOCCARDO, Lucio +3 more
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Scaling in Nonlinear Parabolic Equations
Journal of Mathematical Analysis and Applications, 1999 The Cauchy problem for parabolic equations with quadratic nonlinearity is studied. We investigate the existence of global-in-time solutions and their large-time behavior assuming some scaling property of the equation as well as of the norm of the Banach space in which the solutions are constructed.
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Parabolic equations with nonlinear singularities [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pedro J. Martinez Aparicio +1 more
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Carleman inequality for a class of super strong degenerate parabolic operators and applications
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can not be removed
Bruno Sérgio Araújo +2 more
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Nonlinear parabolic equations, relaxation and roughness
Bulletin des Sciences Mathématiques, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aubin, Thierry +2 more
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A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem
Journal of Inequalities and Applications, 2018 In this paper, we investigate the spectral approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control problem is presented. We construct a fully discrete
Lin Li +4 more
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