Ebook: Progress in Partial Differential Equations: Asymptotic Profiles, Regularity and Well-Posedness

Progress in Partial Differential Equations is devoted to modern topics in the theory of partial differential equations. It consists of both original articles and survey papers covering a wide scope of research topics in partial differential equations and their applications. The contributors were participants of the 8th ISAAC congress in Moscow in 2011 or are members of the PDE interest group of the ISAAC society.

This volume is addressed to graduate students at various levels as well as researchers in partial differential equations and related fields. The readers will find this an excellent resource of both introductory and advanced material. The key topics are:

• Linear hyperbolic equations and systems (scattering, symmetrisers)
• Non-linear wave models (global existence, decay estimates, blow-up)
• Evolution equations (control theory, well-posedness, smoothing)
• Elliptic equations (uniqueness, non-uniqueness, positive solutions)
• Special models from applications (Kirchhoff equation, Zakharov-Kuznetsov equation, thermoelasticity)

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Progress in Partial Differential Equations is devoted to modern topics in the theory of partial differential equations. It consists of both original articles and survey papers covering a wide scope of research topics in partial differential equations and their applications. The contributors were participants of the 8th ISAAC congress in Moscow in 2011 or are members of the PDE interest group of the ISAAC society.

This volume is addressed to graduate students at various levels as well as researchers in partial differential equations and related fields. The reader will find this an excellent resource of both introductory and advanced material. The key topics are:

• Linear hyperbolic equations and systems (scattering, symmetrisers)
• Non-linear wave models (global existence, decay estimates, blow-up)
• Evolution equations (control theory, well-posedness, smoothing)
• Elliptic equations (uniqueness, non-uniqueness, positive solutions)
• Special models from applications (Kirchhoff equation, Zakharov-Kuznetsov equation, thermoelasticity)

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Progress in Partial Differential Equations is devoted to modern topics in the theory of partial differential equations. It consists of both original articles and survey papers covering a wide scope of research topics in partial differential equations and their applications. The contributors were participants of the 8th ISAAC congress in Moscow in 2011 or are members of the PDE interest group of the ISAAC society.

This volume is addressed to graduate students at various levels as well as researchers in partial differential equations and related fields. The reader will find this an excellent resource of both introductory and advanced material. The key topics are:

• Linear hyperbolic equations and systems (scattering, symmetrisers)
• Non-linear wave models (global existence, decay estimates, blow-up)
• Evolution equations (control theory, well-posedness, smoothing)
• Elliptic equations (uniqueness, non-uniqueness, positive solutions)
• Special models from applications (Kirchhoff equation, Zakharov-Kuznetsov equation, thermoelasticity)

Content:
Front Matter....Pages I-VIII
Global Existence and Energy Decay of Solutions for a Nondissipative Wave Equation with a Time-Varying Delay Term....Pages 1-26
Non-uniqueness and Uniqueness in the Cauchy Problem of Elliptic and Backward-Parabolic Equations....Pages 27-52
On Internal Regularity of Solutions to the Initial Value Problem for the Zakharov–Kuznetsov Equation....Pages 53-74
Singular Semilinear Elliptic Equations with Subquadratic Gradient Terms....Pages 75-91
On the Parabolic Regime of a Hyperbolic Equation with Weak Dissipation: The Coercive Case....Pages 93-123
H ? Well-Posedness for Degenerate p-Evolution Models of Higher Order with Time-Dependent Coefficients....Pages 125-151
On the Global Solvability for Semilinear Wave Equations with Smooth Time Dependent Propagation Speeds....Pages 153-181
Filippov Solutions to Systems of Ordinary Differential Equations with Delta Function Terms as Summands....Pages 183-200
Resolvent Estimates and Scattering Problems for Schr?dinger, Klein-Gordon and Wave Equations....Pages 201-221
On an Optimal Control Problem for the Wave Equation in One Space Dimension Controlled by Third Type Boundary Data....Pages 223-238
Critical Exponent for the Semilinear Wave Equation with Time or Space Dependent Damping....Pages 239-259
A Note on a Class of Conservative, Well-Posed Linear Control Systems....Pages 261-286
Recent Progress in Smoothing Estimates for Evolution Equations....Pages 287-302
Differentiability of Inverse Operators....Pages 303-320
Solution of the Cauchy Problem for Generalized Euler-Poisson-Darboux Equation by the Method of Fractional Integrals....Pages 321-337
Quasi-symmetrizer and Hyperbolic Equations....Pages 339-366
Thermo-elasticity for Anisotropic Media in Higher Dimensions....Pages 367-407
Global Solutions of Semilinear System of Klein-Gordon Equations in de Sitter Spacetime....Pages 409-444
Back Matter....Pages 445-447

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Progress in Partial Differential Equations is devoted to modern topics in the theory of partial differential equations. It consists of both original articles and survey papers covering a wide scope of research topics in partial differential equations and their applications. The contributors were participants of the 8th ISAAC congress in Moscow in 2011 or are members of the PDE interest group of the ISAAC society.

This volume is addressed to graduate students at various levels as well as researchers in partial differential equations and related fields. The reader will find this an excellent resource of both introductory and advanced material. The key topics are:

• Linear hyperbolic equations and systems (scattering, symmetrisers)
• Non-linear wave models (global existence, decay estimates, blow-up)
• Evolution equations (control theory, well-posedness, smoothing)
• Elliptic equations (uniqueness, non-uniqueness, positive solutions)
• Special models from applications (Kirchhoff equation, Zakharov-Kuznetsov equation, thermoelasticity)

Content:
Front Matter....Pages I-VIII
Global Existence and Energy Decay of Solutions for a Nondissipative Wave Equation with a Time-Varying Delay Term....Pages 1-26
Non-uniqueness and Uniqueness in the Cauchy Problem of Elliptic and Backward-Parabolic Equations....Pages 27-52
On Internal Regularity of Solutions to the Initial Value Problem for the Zakharov–Kuznetsov Equation....Pages 53-74
Singular Semilinear Elliptic Equations with Subquadratic Gradient Terms....Pages 75-91
On the Parabolic Regime of a Hyperbolic Equation with Weak Dissipation: The Coercive Case....Pages 93-123
H ? Well-Posedness for Degenerate p-Evolution Models of Higher Order with Time-Dependent Coefficients....Pages 125-151
On the Global Solvability for Semilinear Wave Equations with Smooth Time Dependent Propagation Speeds....Pages 153-181
Filippov Solutions to Systems of Ordinary Differential Equations with Delta Function Terms as Summands....Pages 183-200
Resolvent Estimates and Scattering Problems for Schr?dinger, Klein-Gordon and Wave Equations....Pages 201-221
On an Optimal Control Problem for the Wave Equation in One Space Dimension Controlled by Third Type Boundary Data....Pages 223-238
Critical Exponent for the Semilinear Wave Equation with Time or Space Dependent Damping....Pages 239-259
A Note on a Class of Conservative, Well-Posed Linear Control Systems....Pages 261-286
Recent Progress in Smoothing Estimates for Evolution Equations....Pages 287-302
Differentiability of Inverse Operators....Pages 303-320
Solution of the Cauchy Problem for Generalized Euler-Poisson-Darboux Equation by the Method of Fractional Integrals....Pages 321-337
Quasi-symmetrizer and Hyperbolic Equations....Pages 339-366
Thermo-elasticity for Anisotropic Media in Higher Dimensions....Pages 367-407
Global Solutions of Semilinear System of Klein-Gordon Equations in de Sitter Spacetime....Pages 409-444
Back Matter....Pages 445-447
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